Question

A class contains 25 students, 13 play tennis, 14 play volleyball, and 1 play neither of these two sports. A student is randomly selected from the class. Determine the probability that the student: (a) plays both tennis and volleyball. (b) plays at least one of these two sports. (c) play volleyball given that he or she does not play tennis. I need the solutions for part c.

Answer 1

total number of students = 25

number of stdents tthat play tennis = 13

number of students that play volleyball = 14

number of students that doesn't play tennis nor volleyball = 1

(a) to look for number of students that plays both tennis and volleyball

Let the number of students that play both games be x

25 = (13-+x) + x + x + (14-x) + 1

25 = 13 - x + x + 14 - x + 1

25 = 28 - x

x = 3

so probability that the student plays both volleyball and tennes = 3/25

(b) probability that the student plays atleast one of the the two sports

to get the probability that the student plays one of the two sports = 1 - probability that neither plays

probability that neither plays = 1/25

probability that the student plays atleast one = 1 - 1/25

= 24/25

(c) Play volleyball given that he or she does not play tennis

Number of students that play volleyball = 14 - 3

= 11

Therefore, the probability that the student only play volleyball = 11/25