Question

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.

Answer 1

Answer: D. 0.309 is the answer

Answer 2

Answer with explanation:

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

Number of voters who does not support this initiative

`=1 -(30)/(100)\\\\=(70)/(100)`

=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

`=_(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`

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