Answer:
The probability the student studies Art and Biology is 0.2143.
Step-by-step explanation:
Denote the events as follows:
A = a students studies Art
B = a students studies Biology
The information provided is:
N = 42
n (A ∩ B) = 9
n (A' ∩ B) = 10
n (A' ∩ B') = 7
Then the number of students who study Art but not Biology is:
n (A ∩ B') = N - n (A ∩ B) - n (A' ∩ B) - n (A' ∩ B')
[tex]=42-10-7-9\\\\=16[/tex]
The number of students who study Art but not Biology is 16.
Compute the probability the student studies Art and Biology as follows:
[tex]P(A\cap B)=\frac{n (A\cap B)}{N}[/tex]
[tex]=\frac{9}{42}\\\\=\frac{3}{14}\\\\=0.2143[/tex]
Thus, the probability the student studies Art and Biology is 0.2143.
