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In a certain Algebra 2 class of 30 students, 14 of them play basketball and 10 of them play baseball. There are 14 students who play neither sport. What is the probability that a student chosen randomly from the class plays both basketball and baseball?

Respuesta :

Answer:

4/15

Step-by-step explanation:

ashishdwivedilVT

The probability that a student is chosen randomly from the class and plays both basketball and baseball is 4/15.

Let us say the number of students who play basketball is n(A) = 14

Let us say the number of students who play baseball is n(B) = 10

Total students = 30

Number of students who do not play any sport = 14

So, the number of students who play at least one sport:

n(A∪B)=30-14 =16

What does the union of two sets represent?

The Union of two sets represents at least one or we can say that the union of two sets is a set containing all elements that are in A or in B (possibly both)

So, n(A∪B) =n(A) + n(B) - n(A∩B)

16 = 14 +10 -  n(A∩B)

n(A∩B) = 24-16

n(A∩B) =8

So, the number of students who play both the games = 8

So, the probability that a student is chosen randomly from the class plays both basketball and baseball = 8/30 =4/15

Hence, the probability that a student is chosen randomly from the class and plays both basketball and baseball is 4/15.

To get more about set theory visit:

https://brainly.com/question/13458417

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