Question

Conditional Probability

Probability and Statistics

cellus

P(A/B) =

=

P(An B)

P(B)

Freshmen

Sophomores

Juniors

Seniors

Boys

3

1

4

2

Girls

7

9

6

5

21

Answer 1

Here, total number of students is = (3+1+4+2+7+9+6+5) = 37

Event A represents Girls and event B represets Seniors.

Number of girls who are senior students is = 5

Number of senior students is = 5+2 = 7.

Now, P(A\cap B) = [Number of girls who are senior students] / [Number of total students]

i.e., P(A\cap B)=\frac{5}{37}

And, P(B) = [Number f senior students] / [Number of total students]

i.e., P(B)=\frac{7}{37}

Then, P(ANB) P(AB) = P(B)

i.e., P(A|B)=\frac{5/37}{7/37}

i.e., P(A|B)=\frac{5}{7}

Therefore, \boldsymbol{P(Girl|Senior)=\frac{5}{7}}

Step-by-step explanation: