Use the following information for questions:
A child is observing squirrels in the park and notices that some are black and some are gray. For the next five squirrels she sees, she counts X = the number of black squirrels. Suppose X is a binomial random variable with n = 5 and p = 0.50.
-What is the probability that she will see exactly two black squirrels out of the five?
A) 0.031
B) 0.156
C) 0.313
D) 0.500

Question

Use the following information for questions:
 A child is observing squirrels in the park and notices that some are black and some are gray. For the next five squirrels she sees, she counts X = the number of black squirrels. Suppose X is a binomial random variable with n = 5 and p = 0.50.
-What is the probability that she will see exactly two black squirrels out of the five?
A) 0.031
B) 0.156
C) 0.313
D) 0.500

Quizplus · Accepted Answer

The probability of seeing exactly two black squirrels out of five, when each squirrel seen has a 0.50 chance of being black, can be calculated using the binomial probability formula: P(X = k) = (n choose k) * p^k * (1-p)^(n-k). For this scenario, n = 5, k = 2, and p = 0.50, so P(X = 2) = (5 choose 2) * (0.50)^2 * (0.50)^(5-2) = 10 * 0.25 * 0.125 = 0.3125, which rounds to 0.313.

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