Answer to Question #160370 in Statistics and Probability for raazki

Question

Forty-five percent of the streets in an area have private guards for security. Three streets are selected at random:

i. What is the probability all three of the selected streets have private guards?

ii. What is the probability none of the three selected streets has private guards?

iii. What is the probability at least one of the selected streets has private guards?

iv. What is the probability at most two of the selected streets have private guards?

Answer 1

i. The probability that all three of the selected streets have private guards is:

$P(3) = 0.45^3 = 0.091.$

ii. The probability that none of the three selected streets has private guards is:

$P(3) = 0.55^3 = 0.166.$

iii. The probability that at least one of the selected streets has private guards is:

$P(1, 2, 3) = 1 - P(0) = 1 - 0.166 = 0.834.$

iv. The probability that at most two of the selected streets have private guards is:

$P(0, 1, 2) = 1 - P(3) = 1 - 0.091 = 0.909.$