Probability of a student playing both basketball and baseball is 7/28
Step-by-step explanation:
Step 1:
It is given the class has 28 students out of which 11 play basketball and 13 play baseball. It is also given that 11 students play neither sport.
Total number of students = 28
Students playing neither sport = 11
Students playing at least one sport = 28 - 11 = 17
Step 2:
Let N(Basketball) denote the number of students playing basketball and N(Baseball) denote the number of people playing baseball.
Then N(Basketball U Baseball) denotes the total number of students playing basketball and baseball and N(Basketball ∩ Baseball) denotes playing both basketball and baseball.
Since the number of students playing at least one sport is 17, N (Basketball U Baseball) = 17.
N (Basketball U Baseball) = N(Basketball) + N(Baseball) - N(Basketball ∩ Baseball)
N(Basketball ∩ Baseball) = N(Basketball) + N(Baseball) - N (Basketball U Baseball)
N(Basketball ∩ Baseball) = 11 + 13 - 17 = 7
Step 3:
Number of students playing both basketball and baseball = 7
Total number of students = 28
Probability of a student playing both basketball and baseball is 7/28
Step 4:
Answer:
Probability of a student playing both basketball and baseball is 7/28
