A group of freshmen at a local university consider joining the equestrian team. Thirty-five percent of students choose Western riding, 45% choose dressage, and 40% choose jumping. Fifteen percent choose both dressage and jumping, while 15% choose Western and dressage. No one chooses Western and jumping. There are no horses suitable for two styles, and each student is assigned to one horse. If two students decide to join the team, what is the probability that one student joins jumping only and the other student joins the Western team, if they independently decide?
A)0.175
B)0.125
C)0.0375
D)0.105

Question

Quizplus · Accepted Answer

The probability of one student joining jumping only is the probability of joining jumping minus the probability of joining both jumping and dressage, which is 40% - 15% = 25%. The probability of another student joining the Western team is 35%. Since the events are independent, the probability of both events happening is the sum of the probability of one student joining jumping only and then the other joining Western, plus the probability of one joining Western and then the other joining jumping only. This is calculated as (25% * 35%) + (35% * 25%) = 0.0875 + 0.0875 = 0.175.

A Group of Freshmen at a Local University Consider Joining