Question 10 Score: 0 of 4 points In a population where \( 19 \% \) of voters prefer Candidate A , an organization conducts a poll of 9 voters. Find the probability that 4 of the 9 voters will prefer Candidate A . Probability: Enter your answer (Report answer accurate to 4 decimal places.)

To find the probability that exactly 4 out of 9 voters prefer Candidate A, we can use the binomial probability formula: \[ P(X = k) = \binom{n}{k} p^k (1-p)^{n-k} \] where: - \( n \) is the total number of trials (voters surveyed), which is 9, - \( k \) is the number of successful trials (voters who prefer Candidate A), which is 4, - \( p \) is the probability of success (voting for Candidate A), which is 0.19, - \( (1 - p) \) is the probability of failure (not voting for Candidate A), which is 0.81. Now, calculating \( P(X = 4) \): \[ P(X = 4) = \binom{9}{4} (0.19)^4 (0.81)^{9-4} \] Calculating each component: 1. Calculate \( \binom{9}{4} \): \[ \binom{9}{4} = \frac{9!}{4!(9-4)!} = \frac{9 \times 8 \times 7 \times 6}{4 \times 3 \times 2 \times 1} = 126 \] 2. Calculate \( (0.19)^4 \): \[ (0.19)^4 \approx 0.001656 \] 3. Calculate \( (0.81)^5 \): \[ (0.81)^5 \approx 0.348678 \] Now, putting it all together: \[ P(X = 4) = 126 \times 0.001656 \times 0.348678 \approx 0.0730 \] Therefore, the probability that exactly 4 out of 9 voters will prefer Candidate A is approximately: **0.0730** (accurate to four decimal places)