Question

Sports of the 25 baseball players on the baltimore orioles 2005 roster, 17 threw right handed, 12 were over 30 years old, and 9 both threw right handed and were over 30 years old. How many players on the team neither threw right handed nor were over 30 years old?

Answer 1

Answer: 5

Explanation:

Let R be the event that players threw right-handed.

Let O be the event that players were over 30 years old.

Given: Total players = 25

n(R) = 17 , n(O) = 12 , n(R and O)=9

According to the probability formula,

n(R or O) = n(R)+n(O)-n(R and O)

⇒ n(R or O) =17+12-9

⇒ n(R or O) = 20

Now , n(neither R nor O) = Total - n(R or O)

= 25-20

=5

Hence, the number of players on the team neither threw right-handed nor were over 30 years old = 5