\begin{tabular}{l}\( \begin{array}{l}\text { Recent polls suggest that a probability of about } 0.25 \text { of adults } \\ \text { would say they are afraid of heights. Suppose this probability is } \\ \text { true for all adults. Assume responses from different individuals } \\ \text { are independent. }\end{array} \begin{array}{l}\text { 9. What is the probability of having none of } \\ \text { (he } 5 \text { randomly selected adults say that } \\ \text { they are afraid of heights? Round answer } \\ \text { to the nearest thousandths (three decimal } \\ \text { places) }\end{array} \) \\ \( \begin{array}{l}\text { Type a response }\end{array} \) \\ \hline\end{tabular}
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To find the probability that none of the 5 randomly selected adults say they are afraid of heights, we can use the complement of the probability that an adult is afraid of heights. Since the probability of an adult being afraid of heights is \(0.25\), the probability that an adult is not afraid of heights is \(1 - 0.25 = 0.75\). Now, we need to raise this probability to the power of the number of individuals, due to the independence of their responses: \[ P(\text{none afraid}) = (0.75)^5 \] Calculating it: \[ (0.75)^5 = 0.2373046875 \] Rounding to the nearest thousandths, we get: \[ \text{Probability} \approx 0.237 \]
