In a group of 25 students, 6 study both Art and Biology. 10 study Biology but not Art. 3 study neither subject. Given that a randomly selected student studies Art, what is the probability the student studies Art and Biology?

Probability that the student studies Art and biology is; P(A n B) = ½

We are given;

Total number of students in the group; n = 25 students

Number that study both art and biology; n(A u B) = 6

Number that study biology but not art; n(B u A') = 10

Number that study none of the 3 subjects; n(A' u B') = 3

Now;

Number that study only arts is; n(A n B') = 25 - 6 - 10 - 3 = 6

Since n(A u B) = 6

Then;

n(A) = n(A u B) + n(A n B')

n(A) = 6 + 6

n(A) = 12

Thus;

Probability that the student studies Art and biology is;

P(A n B) = 6/12

P(A n B) = ½

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1/2

Step-by-step explanation:

There are a total of 25 students. 3 don't study art or biology. 10 study only biology. 6 study both art and biology. This means the remaining students only study art.

1. Calculate the number of students taking art

only art: 25 - 3 - 6 - 10 = 6

number of students taking art and biology: 6

total number of students taking art: 12

2. Calculate the probability

Out of the 12 total students taking art, 6 are in art and biology.

6/12 = 1/2  

40 is the final : )