Question

Find the probability of each event. A class has five boys and nine girls. If the teacher randomly picks six students, what is the probability that he will pick exactly four girls?

Answer 1

Answer:
`(60)/(143)`

Explanation:

Given, A class has five boys and nine girls.

Total students = 5+9=14

Number of ways to choose 6 students out of 14=
`^(14)C_6` [Using combinations]

Number of ways to choose 4 girls out of 6 (4 girls + 2 boys = 6 ) =
`^(9)C_4*\ ^(5)C_2`

If the teacher randomly picks six students, then the probability that he will pick exactly four girls:-

`(^(9)C_4* \ ^(5)C_2)/(^(14)C_6)`

`=((9!)/(4!5!)*(5!)/(2!3!))/((14!)/(6!8!))\\\\=(1260)/(3003)\\\\=(60)/(143)`

hence, the required probability =
`(60)/(143)` .