Question

In a group of 42 students, 10 study both Art and Biology.

13 study Biology but not Art.
7 study neither subject.
Given that a randomly selected student studies Art, what is the probability the student studies Art and Biology?

Answer 1

given:

in a group of 42 students 10 students study both, 13 study only biology and 7 study neither of the subject.

to find:

the probability of the students who studies art and biology.

solution:

A= students study art

B= students study biology

N=42

n (ANB)= 10

n (A'NB)= 13

n (A'NB')= 7

the number of students who study only art:

n (ANB')= N- n(ANB) - n(A'NB) - n(A'NB')

= 42.10 - 13 - 7

= 12

the number of students who study only art:

= 16

p (ANB)= n (ANB)/N

= 10/40

= 0.238

probability the student who studies art and biology is 0.238.