Answer
a) Probability that all five members on the committee will be girls = (143/2926) = 0.0489
b) Probability that all five members on the committee will be boys = (1/209) = 0.00478
c) Probability there will be at least 1 girl on the committee = (208/209) = 0.995
Step-by-step explanation
The probability of an event is calculated as the number of elements in that event divided by the total number of elements in the sample space.
For this question,
Total number of ways we can select a committee of 5 students from 9 boys and 13 girls = 22C5 = ²²C₅ = 26,334
a) Number of ways of selecting only girls in the committee of 5 = 13C5 = ¹³C₅ = 1,287
Probability that all five members on the committee will be girls = (1287/26334) = (143/2926) = 0.0489
b) Number of ways of selecting only boys in the committee of 5 = ⁹C₅ = 126
Probability that all five members on the committee will be boys = (126/26334) = (1/209) = 0.00478
c) Probability there will be at least 1 girl on the committee
= 1 - (Probability that there will be no girl on the committee)
= 1 - (Probability that there will only boys on the committee)
= 1 - (1/209)
= (208/209)
= 0.995