Probability

Question

Suppose 40% of a large population of registered voters favor the candidate John. A random sample of n=5 voters will be selected, and X, the number favoring John out of 5, is to be observed. What is the probability of getting no one who favors John(i.e. P(X = 0) )?

Answer 1

The probability that each pick favors somebody other than John = 0.6

Since the population is large, the probability that the random sample of n=5 entirely disfavors John = 0.6⁵=0.07776