Question

in a certain town, 65% of the voters support a school referendum up for a vote. if 5 voters are asked for their opinion, what is the probability that at least 1 of the 5 will not support the referendum? 0.0053 0.1160 0.8840 0.9947

Explanation:

Step1: Find the probability that all 5 support

The probability that a voter supports is \(p = 0.65\). The probability that all 5 support is \(P(X = 5)\) using the binomial formula \(P(X=k)=C(n,k)\times p^{k}\times(1 - p)^{n - k}\), where \(n = 5,k = 5\). \(C(5,5)=\frac{5!}{5!(5 - 5)!}=1\), so \(P(X = 5)=1\times(0.65)^{5}\times(1 - 0.65)^{0}=(0.65)^{5}\approx0.0053\)

Step2: Use the complement rule

The probability that at least 1 does not support is \(P(X\geq1)=1 - P(X = 0)\) (equivalent to \(1 - P(\text{all support})\)). Since \(P(\text{all support})\approx0.0053\), then \(P(X\geq1)=1-0.0053 = 0.9947\)

Answer:

0.9947 (the fourth option)