According to a poll, 30% of voters support a ballot initiative. Hans randomly surveys 5 voters. What is the probability that exactly 2 voters will be in favor of the ballot initiative? Round the answer to the nearest thousandth. P (k successes) = Subscript n Baseline C Subscript k Baseline p Superscript k Baseline (1 minus p) Superscript n minus k. Subscript n Baseline C Subscript k Baseline = StartFraction n factorial Over (n minus k) factorial times k factorial EndFraction 0.024 0.031 0.132 0.309

Answer with explanation:

Number of voters who support ballot initiative = 30 %=0.30

Number of voters who does not support this initiative

\begin{gathered}=1 -\frac{30}{100}=\frac{70}{100}\end{gathered}

=1−

100

30

=

100

70

=0.70

Number of voters selected for Surveying =5

Probability that exactly 2 voters will be in favor of the ballot initiative is given by ,if P denotes Success and Q denotes failure

\begin{gathered}=_{2}^{5}\textrm{C}*P^2*Q^3=10*(0.3)^2*(0.7)^3=10* 0.09*0.343=0.9*0.343=0.3087\end{gathered}

=

2

5

C∗P

2

∗Q

3

=10∗(0.3)

2

∗(0.7)

3

=10∗0.09∗0.343

=0.9∗0.343

=0.3087

If we round up to nearest thousandth, Required Probability = 0.309

0.02040816326