Question

In a certain congressional district, it is known that 30% of the registered voters classify themselves as conservatives. If ten registered voters are selected at random from this district, what is the probability that two of them will be conservatives? (Round your answer to four decimal places.)

Answer 1

In a certain district, 30% registered votes classify themselves as conservatists;
Thus, probability of a registered voter being a conservatist = p = 3/10
Probability of not being a conservatist = q = 1-p = 7/10;

So, in a random sample of ten registered votes, probability of finding exactly two of them to be conservatist can be found out by applying binomial distribution of probability
P(p=2 when n=10) is = 10C2 (3/10)² (7/10)⁸ = 10*9*8!/ 2*8! (9) (7)⁸ / 10¹⁰ = 45 *9*7⁸ / 10¹⁰


Thus, in a random sample of ten registered votes, probability of finding exactly two of them to be conservatist is
=45 *9*7⁸ / 10¹⁰