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. 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 1

The probability that exactly 2 voters will be in favor of the ballot initiative is 0.309.

Given

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

Number of voters who does not support this initiative = 1 - 0.30 = 0.70

Number of voters selected for Surveying = 5

What is probability?

The probability of success and failure remain the same throughout the trials.

The probability that exactly 2 voters will be in favor of the ballot initiative is given by;

If P denotes Success and Q denotes failure;

$\rm = ^{5}C_2 \times (0.3)^2 \times (0.70)^3\\\\= 10 \times 0.09 \times 0.343\\\\= 0.309$

Hence, the probability that exactly 2 voters will be in favor of the ballot initiative is 0.309.

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