15. 5.2 HW Part 2 of \( 3.2 .27-T \) Based on a survey, \( 33 \% \) of likely voters would be willing to vote by internet instead of the in-person traditional method of voting. For each of the following, assume that 12 likely voters are randomly selected. Complete parts (a) through (c) below. b. If 9 of the selected voters would do internet voting, is 9 significantly high? Why or why not? 20.67 of 22 points Select the correct choice below and fill in the answer box within your choice. (Round to five decimal places as needed.) A. Yes, because the probability of 9 or more is \( \square \), which is not low. B. No, because the probability of 9 or more is \( \square \), which is not low. C. No, because the probability of 9 or more is \( \square \), which is low. D. Yes, because the probability of 9 or more is \( \square \), which is low.

To determine if 9 is significantly high, we need to calculate the probability of getting 9 or more voters who would do internet voting out of 12 selected voters. Given that 33% of likely voters would be willing to vote by internet, we can calculate the probability of getting 9 or more voters who would do internet voting using the binomial distribution formula. The probability of getting exactly \( k \) successes in \( n \) trials, where the probability of success in each trial is \( p \), is given by the binomial distribution formula: \[ P(X = k) = \binom{n}{k} p^k (1-p)^{n-k} \] In this case, \( n = 12 \), \( k = 9 \), and \( p = 0.33 \). Let's calculate the probability of getting 9 or more voters who would do internet voting: \[ P(X \geq 9) = 1 - P(X < 9) \] \[ P(X < 9) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8) \] We will calculate each of these probabilities using the binomial distribution formula and then sum them up to find the probability of getting 9 or more voters who would do internet voting. Let's calculate the probabilities: Calculate the value by following steps: - step0: Calculate: \(1-\left(0.33^{0}\left(1-0.33\right)^{12}+0.33^{1}\left(1-0.33\right)^{11}+0.33^{2}\left(1-0.33\right)^{10}+0.33^{3}\left(1-0.33\right)^{9}+0.33^{4}\left(1-0.33\right)^{8}+0.33^{5}\left(1-0.33\right)^{7}+0.33^{6}\left(1-0.33\right)^{6}+0.33^{7}\left(1-0.33\right)^{5}+0.33^{8}\left(1-0.33\right)^{4}\right)\) - step1: Evaluate the power: \(1-\left(1\times \left(1-0.33\right)^{12}+0.33^{1}\left(1-0.33\right)^{11}+0.33^{2}\left(1-0.33\right)^{10}+0.33^{3}\left(1-0.33\right)^{9}+0.33^{4}\left(1-0.33\right)^{8}+0.33^{5}\left(1-0.33\right)^{7}+0.33^{6}\left(1-0.33\right)^{6}+0.33^{7}\left(1-0.33\right)^{5}+0.33^{8}\left(1-0.33\right)^{4}\right)\) - step2: Subtract the numbers: \(1-\left(1\times 0.67^{12}+0.33^{1}\left(1-0.33\right)^{11}+0.33^{2}\left(1-0.33\right)^{10}+0.33^{3}\left(1-0.33\right)^{9}+0.33^{4}\left(1-0.33\right)^{8}+0.33^{5}\left(1-0.33\right)^{7}+0.33^{6}\left(1-0.33\right)^{6}+0.33^{7}\left(1-0.33\right)^{5}+0.33^{8}\left(1-0.33\right)^{4}\right)\) - step3: Subtract the numbers: \(1-\left(1\times 0.67^{12}+0.33^{1}\times 0.67^{11}+0.33^{2}\left(1-0.33\right)^{10}+0.33^{3}\left(1-0.33\right)^{9}+0.33^{4}\left(1-0.33\right)^{8}+0.33^{5}\left(1-0.33\right)^{7}+0.33^{6}\left(1-0.33\right)^{6}+0.33^{7}\left(1-0.33\right)^{5}+0.33^{8}\left(1-0.33\right)^{4}\right)\) - step4: Subtract the numbers: \(1-\left(1\times 0.67^{12}+0.33^{1}\times 0.67^{11}+0.33^{2}\times 0.67^{10}+0.33^{3}\left(1-0.33\right)^{9}+0.33^{4}\left(1-0.33\right)^{8}+0.33^{5}\left(1-0.33\right)^{7}+0.33^{6}\left(1-0.33\right)^{6}+0.33^{7}\left(1-0.33\right)^{5}+0.33^{8}\left(1-0.33\right)^{4}\right)\) - step5: Subtract the numbers: \(1-\left(1\times 0.67^{12}+0.33^{1}\times 0.67^{11}+0.33^{2}\times 0.67^{10}+0.33^{3}\times 0.67^{9}+0.33^{4}\left(1-0.33\right)^{8}+0.33^{5}\left(1-0.33\right)^{7}+0.33^{6}\left(1-0.33\right)^{6}+0.33^{7}\left(1-0.33\right)^{5}+0.33^{8}\left(1-0.33\right)^{4}\right)\) - step6: Subtract the numbers: \(1-\left(1\times 0.67^{12}+0.33^{1}\times 0.67^{11}+0.33^{2}\times 0.67^{10}+0.33^{3}\times 0.67^{9}+0.33^{4}\times 0.67^{8}+0.33^{5}\left(1-0.33\right)^{7}+0.33^{6}\left(1-0.33\right)^{6}+0.33^{7}\left(1-0.33\right)^{5}+0.33^{8}\left(1-0.33\right)^{4}\right)\) - step7: Subtract the numbers: \(1-\left(1\times 0.67^{12}+0.33^{1}\times 0.67^{11}+0.33^{2}\times 0.67^{10}+0.33^{3}\times 0.67^{9}+0.33^{4}\times 0.67^{8}+0.33^{5}\times 0.67^{7}+0.33^{6}\left(1-0.33\right)^{6}+0.33^{7}\left(1-0.33\right)^{5}+0.33^{8}\left(1-0.33\right)^{4}\right)\) - step8: Subtract the numbers: \(1-\left(1\times 0.67^{12}+0.33^{1}\times 0.67^{11}+0.33^{2}\times 0.67^{10}+0.33^{3}\times 0.67^{9}+0.33^{4}\times 0.67^{8}+0.33^{5}\times 0.67^{7}+0.33^{6}\times 0.67^{6}+0.33^{7}\left(1-0.33\right)^{5}+0.33^{8}\left(1-0.33\right)^{4}\right)\) - step9: Subtract the numbers: \(1-\left(1\times 0.67^{12}+0.33^{1}\times 0.67^{11}+0.33^{2}\times 0.67^{10}+0.33^{3}\times 0.67^{9}+0.33^{4}\times 0.67^{8}+0.33^{5}\times 0.67^{7}+0.33^{6}\times 0.67^{6}+0.33^{7}\times 0.67^{5}+0.33^{8}\left(1-0.33\right)^{4}\right)\) - step10: Subtract the numbers: \(1-\left(1\times 0.67^{12}+0.33^{1}\times 0.67^{11}+0.33^{2}\times 0.67^{10}+0.33^{3}\times 0.67^{9}+0.33^{4}\times 0.67^{8}+0.33^{5}\times 0.67^{7}+0.33^{6}\times 0.67^{6}+0.33^{7}\times 0.67^{5}+0.33^{8}\times 0.67^{4}\right)\) - step11: Convert the expressions: \(1-\left(1\times \left(\frac{67}{100}\right)^{12}+0.33^{1}\times 0.67^{11}+0.33^{2}\times 0.67^{10}+0.33^{3}\times 0.67^{9}+0.33^{4}\times 0.67^{8}+0.33^{5}\times 0.67^{7}+0.33^{6}\times 0.67^{6}+0.33^{7}\times 0.67^{5}+0.33^{8}\times 0.67^{4}\right)\) - step12: Calculate: \(1-\left(1\times \left(\frac{67}{100}\right)^{12}+\frac{33}{100}\times 0.67^{11}+0.33^{2}\times 0.67^{10}+0.33^{3}\times 0.67^{9}+0.33^{4}\times 0.67^{8}+0.33^{5}\times 0.67^{7}+0.33^{6}\times 0.67^{6}+0.33^{7}\times 0.67^{5}+0.33^{8}\times 0.67^{4}\right)\) - step13: Convert the expressions: \(1-\left(1\times \left(\frac{67}{100}\right)^{12}+\frac{33}{100}\left(\frac{67}{100}\right)^{11}+0.33^{2}\times 0.67^{10}+0.33^{3}\times 0.67^{9}+0.33^{4}\times 0.67^{8}+0.33^{5}\times 0.67^{7}+0.33^{6}\times 0.67^{6}+0.33^{7}\times 0.67^{5}+0.33^{8}\times 0.67^{4}\right)\) - step14: Convert the expressions: \(1-\left(1\times \left(\frac{67}{100}\right)^{12}+\frac{33}{100}\left(\frac{67}{100}\right)^{11}+\left(\frac{33}{100}\right)^{2}\times 0.67^{10}+0.33^{3}\times 0.67^{9}+0.33^{4}\times 0.67^{8}+0.33^{5}\times 0.67^{7}+0.33^{6}\times 0.67^{6}+0.33^{7}\times 0.67^{5}+0.33^{8}\times 0.67^{4}\right)\) - step15: Convert the expressions: \(1-\left(1\times \left(\frac{67}{100}\right)^{12}+\frac{33}{100}\left(\frac{67}{100}\right)^{11}+\left(\frac{33}{100}\right)^{2}\left(\frac{67}{100}\right)^{10}+0.33^{3}\times 0.67^{9}+0.33^{4}\times 0.67^{8}+0.33^{5}\times 0.67^{7}+0.33^{6}\times 0.67^{6}+0.33^{7}\times 0.67^{5}+0.33^{8}\times 0.67^{4}\right)\) - step16: Convert the expressions: \(1-\left(1\times \left(\frac{67}{100}\right)^{12}+\frac{33}{100}\left(\frac{67}{100}\right)^{11}+\left(\frac{33}{100}\right)^{2}\left(\frac{67}{100}\right)^{10}+\left(\frac{33}{100}\right)^{3}\times 0.67^{9}+0.33^{4}\times 0.67^{8}+0.33^{5}\times 0.67^{7}+0.33^{6}\times 0.67^{6}+0.33^{7}\times 0.67^{5}+0.33^{8}\times 0.67^{4}\right)\) - step17: Convert the expressions: \(1-\left(1\times \left(\frac{67}{100}\right)^{12}+\frac{33}{100}\left(\frac{67}{100}\right)^{11}+\left(\frac{33}{100}\right)^{2}\left(\frac{67}{100}\right)^{10}+\left(\frac{33}{100}\right)^{3}\left(\frac{67}{100}\right)^{9}+0.33^{4}\times 0.67^{8}+0.33^{5}\times 0.67^{7}+0.33^{6}\times 0.67^{6}+0.33^{7}\times 0.67^{5}+0.33^{8}\times 0.67^{4}\right)\) - step18: Convert the expressions: \(1-\left(1\times \left(\frac{67}{100}\right)^{12}+\frac{33}{100}\left(\frac{67}{100}\right)^{11}+\left(\frac{33}{100}\right)^{2}\left(\frac{67}{100}\right)^{10}+\left(\frac{33}{100}\right)^{3}\left(\frac{67}{100}\right)^{9}+\left(\frac{33}{100}\right)^{4}\times 0.67^{8}+0.33^{5}\times 0.67^{7}+0.33^{6}\times 0.67^{6}+0.33^{7}\times 0.67^{5}+0.33^{8}\times 0.67^{4}\right)\) - step19: Convert the expressions: \(1-\left(1\times \left(\frac{67}{100}\right)^{12}+\frac{33}{100}\left(\frac{67}{100}\right)^{11}+\left(\frac{33}{100}\right)^{2}\left(\frac{67}{100}\right)^{10}+\left(\frac{33}{100}\right)^{3}\left(\frac{67}{100}\right)^{9}+\left(\frac{33}{100}\right)^{4}\left(\frac{67}{100}\right)^{8}+0.33^{5}\times 0.67^{7}+0.33^{6}\times 0.67^{6}+0.33^{7}\times 0.67^{5}+0.33^{8}\times 0.67^{4}\right)\) - step20: Convert the expressions: \(1-\left(1\times \left(\frac{67}{100}\right)^{12}+\frac{33}{100}\left(\frac{67}{100}\right)^{11}+\left(\frac{33}{100}\right)^{2}\left(\frac{67}{100}\right)^{10}+\left(\frac{33}{100}\right)^{3}\left(\frac{67}{100}\right)^{9}+\left(\frac{33}{100}\right)^{4}\left(\frac{67}{100}\right)^{8}+\left(\frac{33}{100}\right)^{5}\times 0.67^{7}+0.33^{6}\times 0.67^{6}+0.33^{7}\times 0.67^{5}+0.33^{8}\times 0.67^{4}\right)\) - step21: Convert the expressions: \(1-\left(1\times \left(\frac{67}{100}\right)^{12}+\frac{33}{100}\left(\frac{67}{100}\right)^{11}+\left(\frac{33}{100}\right)^{2}\left(\frac{67}{100}\right)^{10}+\left(\frac{33}{100}\right)^{3}\left(\frac{67}{100}\right)^{9}+\left(\frac{33}{100}\right)^{4}\left(\frac{67}{100}\right)^{8}+\left(\frac{33}{100}\right)^{5}\left(\frac{67}{100}\right)^{7}+0.33^{6}\times 0.67^{6}+0.33^{7}\times 0.67^{5}+0.33^{8}\times 0.67^{4}\right)\) - step22: Convert the expressions: \(1-\left(1\times \left(\frac{67}{100}\right)^{12}+\frac{33}{100}\left(\frac{67}{100}\right)^{11}+\left(\frac{33}{100}\right)^{2}\left(\frac{67}{100}\right)^{10}+\left(\frac{33}{100}\right)^{3}\left(\frac{67}{100}\right)^{9}+\left(\frac{33}{100}\right)^{4}\left(\frac{67}{100}\right)^{8}+\left(\frac{33}{100}\right)^{5}\left(\frac{67}{100}\right)^{7}+\left(\frac{33}{100}\right)^{6}\times 0.67^{6}+0.33^{7}\times 0.67^{5}+0.33^{8}\times 0.67^{4}\right)\) - step23: Convert the expressions: \(1-\left(1\times \left(\frac{67}{100}\right)^{12}+\frac{33}{100}\left(\frac{67}{100}\right)^{11}+\left(\frac{33}{100}\right)^{2}\left(\frac{67}{100}\right)^{10}+\left(\frac{33}{100}\right)^{3}\left(\frac{67}{100}\right)^{9}+\left(\frac{33}{100}\right)^{4}\left(\frac{67}{100}\right)^{8}+\left(\frac{33}{100}\right)^{5}\left(\frac{67}{100}\right)^{7}+\left(\frac{33}{100}\right)^{6}\left(\frac{67}{100}\right)^{6}+0.33^{7}\times 0.67^{5}+0.33^{8}\times 0.67^{4}\right)\) - step24: Convert the expressions: \(1-\left(1\times \left(\frac{67}{100}\right)^{12}+\frac{33}{100}\left(\frac{67}{100}\right)^{11}+\left(\frac{33}{100}\right)^{2}\left(\frac{67}{100}\right)^{10}+\left(\frac{33}{100}\right)^{3}\left(\frac{67}{100}\right)^{9}+\left(\frac{33}{100}\right)^{4}\left(\frac{67}{100}\right)^{8}+\left(\frac{33}{100}\right)^{5}\left(\frac{67}{100}\right)^{7}+\left(\frac{33}{100}\right)^{6}\left(\frac{67}{100}\right)^{6}+\left(\frac{33}{100}\right)^{7}\times 0.67^{5}+0.33^{8}\times 0.67^{4}\right)\) - step25: Convert the expressions: \(1-\left(1\times \left(\frac{67}{100}\right)^{12}+\frac{33}{100}\left(\frac{67}{100}\right)^{11}+\left(\frac{33}{100}\right)^{2}\left(\frac{67}{100}\right)^{10}+\left(\frac{33}{100}\right)^{3}\left(\frac{67}{100}\right)^{9}+\left(\frac{33}{100}\right)^{4}\left(\frac{67}{100}\right)^{8}+\left(\frac{33}{100}\right)^{5}\left(\frac{67}{100}\right)^{7}+\left(\frac{33}{100}\right)^{6}\left(\frac{67}{100}\right)^{6}+\left(\frac{33}{100}\right)^{7}\left(\frac{67}{100}\right)^{5}+0.33^{8}\times 0.67^{4}\right)\) - step26: Convert the expressions: \(1-\left(1\times \left(\frac{67}{100}\right)^{12}+\frac{33}{100}\left(\frac{67}{100}\right)^{11}+\left(\frac{33}{100}\right)^{2}\left(\frac{67}{100}\right)^{10}+\left(\frac{33}{100}\right)^{3}\left(\frac{67}{100}\right)^{9}+\left(\frac{33}{100}\right)^{4}\left(\frac{67}{100}\right)^{8}+\left(\frac{33}{100}\right)^{5}\left(\frac{67}{100}\right)^{7}+\left(\frac{33}{100}\right)^{6}\left(\frac{67}{100}\right)^{6}+\left(\frac{33}{100}\right)^{7}\left(\frac{67}{100}\right)^{5}+\left(\frac{33}{100}\right)^{8}\times 0.67^{4}\right)\) - step27: Convert the expressions: \(1-\left(1\times \left(\frac{67}{100}\right)^{12}+\frac{33}{100}\left(\frac{67}{100}\right)^{11}+\left(\frac{33}{100}\right)^{2}\left(\frac{67}{100}\right)^{10}+\left(\frac{33}{100}\right)^{3}\left(\frac{67}{100}\right)^{9}+\left(\frac{33}{100}\right)^{4}\left(\frac{67}{100}\right)^{8}+\left(\frac{33}{100}\right)^{5}\left(\frac{67}{100}\right)^{7}+\left(\frac{33}{100}\right)^{6}\left(\frac{67}{100}\right)^{6}+\left(\frac{33}{100}\right)^{7}\left(\frac{67}{100}\right)^{5}+\left(\frac{33}{100}\right)^{8}\left(\frac{67}{100}\right)^{4}\right)\) - step28: Multiply: \(1-\left(\left(\frac{67}{100}\right)^{12}+\frac{33}{100}\left(\frac{67}{100}\right)^{11}+\left(\frac{33}{100}\right)^{2}\left(\frac{67}{100}\right)^{10}+\left(\frac{33}{100}\right)^{3}\left(\frac{67}{100}\right)^{9}+\left(\frac{33}{100}\right)^{4}\left(\frac{67}{100}\right)^{8}+\left(\frac{33}{100}\right)^{5}\left(\frac{67}{100}\right)^{7}+\left(\frac{33}{100}\right)^{6}\left(\frac{67}{100}\right)^{6}+\left(\frac{33}{100}\right)^{7}\left(\frac{67}{100}\right)^{5}+\left(\frac{33}{100}\right)^{8}\left(\frac{67}{100}\right)^{4}\right)\) - step29: Multiply the numbers: \(1-\left(\left(\frac{67}{100}\right)^{12}+\frac{33\times 67^{11}}{100^{12}}+\left(\frac{33}{100}\right)^{2}\left(\frac{67}{100}\right)^{10}+\left(\frac{33}{100}\right)^{3}\left(\frac{67}{100}\right)^{9}+\left(\frac{33}{100}\right)^{4}\left(\frac{67}{100}\right)^{8}+\left(\frac{33}{100}\right)^{5}\left(\frac{67}{100}\right)^{7}+\left(\frac{33}{100}\right)^{6}\left(\frac{67}{100}\right)^{6}+\left(\frac{33}{100}\right)^{7}\left(\frac{67}{100}\right)^{5}+\left(\frac{33}{100}\right)^{8}\left(\frac{67}{100}\right)^{4}\right)\) - step30: Multiply the numbers: \(1-\left(\left(\frac{67}{100}\right)^{12}+\frac{33\times 67^{11}}{100^{12}}+\frac{33^{2}}{100^{2}}\times \frac{67^{10}}{100^{10}}+\left(\frac{33}{100}\right)^{3}\left(\frac{67}{100}\right)^{9}+\left(\frac{33}{100}\right)^{4}\left(\frac{67}{100}\right)^{8}+\left(\frac{33}{100}\right)^{5}\left(\frac{67}{100}\right)^{7}+\left(\frac{33}{100}\right)^{6}\left(\frac{67}{100}\right)^{6}+\left(\frac{33}{100}\right)^{7}\left(\frac{67}{100}\right)^{5}+\left(\frac{33}{100}\right)^{8}\left(\frac{67}{100}\right)^{4}\right)\) - step31: Multiply the numbers: \(1-\left(\left(\frac{67}{100}\right)^{12}+\frac{33\times 67^{11}}{100^{12}}+\frac{33^{2}}{100^{2}}\times \frac{67^{10}}{100^{10}}+\frac{33^{3}}{100^{3}}\times \frac{67^{9}}{100^{9}}+\left(\frac{33}{100}\right)^{4}\left(\frac{67}{100}\right)^{8}+\left(\frac{33}{100}\right)^{5}\left(\frac{67}{100}\right)^{7}+\left(\frac{33}{100}\right)^{6}\left(\frac{67}{100}\right)^{6}+\left(\frac{33}{100}\right)^{7}\left(\frac{67}{100}\right)^{5}+\left(\frac{33}{100}\right)^{8}\left(\frac{67}{100}\right)^{4}\right)\) - step32: Multiply the numbers: \(1-\left(\left(\frac{67}{100}\right)^{12}+\frac{33\times 67^{11}}{100^{12}}+\frac{33^{2}}{100^{2}}\times \frac{67^{10}}{100^{10}}+\frac{33^{3}}{100^{3}}\times \frac{67^{9}}{100^{9}}+\frac{33^{4}}{100^{4}}\times \frac{67^{8}}{100^{8}}+\left(\frac{33}{100}\right)^{5}\left(\frac{67}{100}\right)^{7}+\left(\frac{33}{100}\right)^{6}\left(\frac{67}{100}\right)^{6}+\left(\frac{33}{100}\right)^{7}\left(\frac{67}{100}\right)^{5}+\left(\frac{33}{100}\right)^{8}\left(\frac{67}{100}\right)^{4}\right)\) - step33: Multiply the numbers: \(1-\left(\left(\frac{67}{100}\right)^{12}+\frac{33\times 67^{11}}{100^{12}}+\frac{33^{2}}{100^{2}}\times \frac{67^{10}}{100^{10}}+\frac{33^{3}}{100^{3}}\times \frac{67^{9}}{100^{9}}+\frac{33^{4}}{100^{4}}\times \frac{67^{8}}{100^{8}}+\frac{33^{5}}{100^{5}}\times \frac{67^{7}}{100^{7}}+\left(\frac{33}{100}\right)^{6}\left(\frac{67}{100}\right)^{6}+\left(\frac{33}{100}\right)^{7}\left(\frac{67}{100}\right)^{5}+\left(\frac{33}{100}\right)^{8}\left(\frac{67}{100}\right)^{4}\right)\) - step34: Multiply the numbers: \(1-\left(\left(\frac{67}{100}\right)^{12}+\frac{33\times 67^{11}}{100^{12}}+\frac{33^{2}}{100^{2}}\times \frac{67^{10}}{100^{10}}+\frac{33^{3}}{100^{3}}\times \frac{67^{9}}{100^{9}}+\frac{33^{4}}{100^{4}}\times \frac{67^{8}}{100^{8}}+\frac{33^{5}}{100^{5}}\times \frac{67^{7}}{100^{7}}+\frac{2211^{6}}{10000^{6}}+\left(\frac{33}{100}\right)^{7}\left(\frac{67}{100}\right)^{5}+\left(\frac{33}{100}\right)^{8}\left(\frac{67}{100}\right)^{4}\right)\) - step35: Multiply the numbers: \(1-\left(\left(\frac{67}{100}\right)^{12}+\frac{33\times 67^{11}}{100^{12}}+\frac{33^{2}}{100^{2}}\times \frac{67^{10}}{100^{10}}+\frac{33^{3}}{100^{3}}\times \frac{67^{9}}{100^{9}}+\frac{33^{4}}{100^{4}}\times \frac{67^{8}}{100^{8}}+\frac{33^{5}}{100^{5}}\times \frac{67^{7}}{100^{7}}+\frac{2211^{6}}{10000^{6}}+\frac{33^{7}}{100^{7}}\times \frac{67^{5}}{100^{5}}+\left(\frac{33}{100}\right)^{8}\left(\frac{67}{100}\right)^{4}\right)\) - step36: Multiply the numbers: \(1-\left(\left(\frac{67}{100}\right)^{12}+\frac{33\times 67^{11}}{100^{12}}+\frac{33^{2}}{100^{2}}\times \frac{67^{10}}{100^{10}}+\frac{33^{3}}{100^{3}}\times \frac{67^{9}}{100^{9}}+\frac{33^{4}}{100^{4}}\times \frac{67^{8}}{100^{8}}+\frac{33^{5}}{100^{5}}\times \frac{67^{7}}{100^{7}}+\frac{2211^{6}}{10000^{6}}+\frac{33^{7}}{100^{7}}\times \frac{67^{5}}{100^{5}}+\frac{33^{8}}{100^{8}}\times \frac{67^{4}}{100^{4}}\right)\) - step37: Add the numbers: \(1-\frac{557800\times 67^{9}+484837\times 33^{4}\times 67^{5}+2211^{6}+33^{8}\times 67^{4}}{100^{12}}\) - step38: Reduce fractions to a common denominator: \(\frac{100^{12}}{100^{12}}-\frac{557800\times 67^{9}+484837\times 33^{4}\times 67^{5}+2211^{6}+33^{8}\times 67^{4}}{100^{12}}\) - step39: Transform the expression: \(\frac{100^{12}-\left(557800\times 67^{9}+484837\times 33^{4}\times 67^{5}+2211^{6}+33^{8}\times 67^{4}\right)}{100^{12}}\) - step40: Remove the parentheses: \(\frac{100^{12}-557800\times 67^{9}-484837\times 33^{4}\times 67^{5}-2211^{6}-33^{8}\times 67^{4}}{100^{12}}\) The probability of getting 9 or more voters who would do internet voting out of 12 selected voters is approximately 0.9839. Since the probability is not low, we can conclude that 9 is significantly high.