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 one black squirrel 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 one black squirrel out of the five?
A) 0.031
B) 0.156
C) 0.313
D) 0.500

Quizplus · Accepted Answer

The probability of seeing exactly one black squirrel out of five, when each squirrel 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). Here, n = 5, k = 1, and p = 0.50. Thus, P(X = 1) = (5 choose 1) * (0.50)^1 * (0.50)^(5-1) = 5 * 0.50 * 0.0625 = 0.156.

Use the Following Information for Questions