512,398 views
20 votes
20 votes
from a group of 9 boys and 13 girls, a committee of 5 students is chosen at random. a. what is the probability that all five members on the committee will be girls? b. what is the probability that all 5 members of the committee will be boys?c. what is the probability there will be at least 1 girl on the committee?

User Sinapcs
by
2.9k points

1 Answer

22 votes
22 votes

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

User Warsong
by
2.5k points