Question

A committee of 4 students is selected at random from a group consisting of 8 boys and 4 girls. Given that there is atleast one girl in committee, calculate the probability that there are exactly 2 girls in the committee. Select the correct answer from above options

Answer 1

let event of getting atleast one girl in committee be`A` A= 1 girl + 2 girl + 3 girl + 4 girl `= .^12C_4 - .^8C_4 ` `= (12 xx 11xx 10 xx 9)/(4 xx 3 xx2) - ( 8 xx7 xx 6 xx 5)/(4 xx 3 xx 2 xx1)` `= 495- 70 = 425` let B be the event of exactly 2 girls in the committee `B= .^4C_2 .^8C_2` `= (4 xx 3)/2 xx( 8 xx7)/2` `= 6 xx 28 = 168` `P(B/A) = (P(B nn A))/(P(A))` `= 168/425` answer