Question

1. There are five Power Rangers. Of the five, three are male (Red, Black, Blue) and two are female (Pink, Yellow.) I randomly select two of the Power Rangers, without replacement.

(a) What is the probability that the Pink Ranger is one of the two selected Power Rangers?

(b) What is the probability at least one of the two selected Power Rangers is female?

(c) Given that at least one of the two selected Power Rangers is female, what is the conditional probability the Pink Ranger is selected?

(d) Are the events “the Pink Ranger is one of the two selected” and “at least one of the two selected Power Rangers is female” independent? Explain why or why not.

Answer 1

Total number of ways in which two Power Rangers can be selected out of five = 5*4 = 20

(a) Number of ways of selection such that one of the selected Power Rangers is Pink Ranger = 1*4 + 4*1 = 8

Thus, the required probability = 8/20 = 0.4

(b) The required probability = 1 - None of the selected Power Rangers is female

= 1 - (3*2)/20 = 0.7

(c) The required probability = 0.4/0.7 = 4/7

(d) No, the given events are not independent.

Since the conditional probability of "the Pink Ranger is one of the two selected" is different when conditioned on "at least one of the two selected Power Rangers is female"