in a certain town, 65% of the voters support a school referendum up for a vote. if 5 voters are asked for…

Explanation:

Step1: Find probability of supporting

The probability that a voter supports the referendum is $p = 0.65$.

Step2: Find probability of not - supporting

The probability that a voter does not support the referendum is $q=1 - p=1 - 0.65 = 0.35$.

Step3: Find probability that all 5 support

The probability that all 5 voters support the referendum is given by the binomial probability formula $P(X = k)=C(n,k)\times p^{k}\times q^{n - k}$, where $n = 5$, $k = 5$, $p = 0.65$, and $q = 0.35$. Since $C(5,5)=\frac{5!}{5!(5 - 5)!}=1$, then $P(X = 5)=1\times(0.65)^{5}\times(0.35)^{0}=(0.65)^{5}=0.00527$.

Step4: Find probability that at least 1 does not support

The probability that at least 1 of the 5 does not support is the complement of the event that all 5 support. Let $A$ be the event that at least 1 does not support. Then $P(A)=1 - P(X = 5)=1-(0.65)^{5}=1 - 0.00527 = 0.99473\approx0.9947$.

Answer:

0.9947