Question

An elementary school has 3 sports clubs: baseball, football, and ice hockey. Those clubs are open to any of the 100 students in the school. There are 36 students play football, 28 play baseball, and 14 play ice hockey. There are 12 students play both football and baseball, 6 play both football and ice hockey, 4 play both baseball and ice hockey. In addition, there are 2 students play all 3 sports.

(a) If a student is chosen randomly, what is the probability that he or she doesn’t play any of the 3 sports?

(b) If a student is chosen randomly, what is the probability that he or she plays only 1 sport?

(c) If 5 students are chosen randomly, what is the probability that 2 of them doesn’t play any sports, and 2 of them play only 1 sport.

Answer 1

From the given information we can draw the Venn diagram as follows :

The area outside the circles = 100 - 20-14-6-10-4-2-2 = 42

a) P( he or she doesn’t play any of the 3 sports ) = 42/100 = 0.42

b) P( he or she plays only 1 sport ) = 20 + 14 + 6 = 40/100 = 0.40

c) P( 2 of them doesn’t play any sports, and 2 of them play only 1 sport )

Doesn’t play any sports ( X ) = 42 ,

Play only 1 sport ( Y ) = 40

P(  X = 2 , Y = 2 )

=

=

=

= 0.1606

Probability that 2 of them doesn’t play any sports, and 2 of them play only 1 sport 0.1606