Personnel selection. Suppose that 6 female and 5 male applicants have been successfully screened for 5 positions. If the 5 positions are filled at random from the 11 finalists, what is the probability of selecting (A) 3 females and 2​ males? ​(B) 4 females and 1​ male? ​(C) 5​ females?

Anish Buchanan 2021-03-07 Answered
Personnel selection. Suppose that 6 female and 5 male applicants have been successfully screened for 5 positions. If the 5 positions are filled at random from the 11 finalists, what is the probability of selecting
(A) 3 females and 2​ males?
​(B) 4 females and 1​ male?
​(C) 5​ females?
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Expert Answer

un4t5o4v
Answered 2021-03-08 Author has 105 answers
Data analysis
Note : As per authoring guidelines, when multiple subparts are posted, then only first three subparts are to be answered.
Given there is selection for a Personnel.
And there are 11 finalists in which 6 are female and 5 are female.
And there are only 5 posts vacant.
To find the probability of selecting as below.
Total ways
Total number of ways of selecting 5 people from 11 finalists is given by,
11P5
=11 × 10 × 9 × 8 ×7
=55.440
Probability is given by the ratio of number of favourable ways to the total number of ways.
Note :
nPr=n !n  r!
A) 3 females and 2​ males
3 females selected from 6 female finalists in 6P3 ways
=6 × 5 ×4
=120
2 males selected from 5 male finalists in 5P2 ways
=5 × 4
=20
Favourable ways =120 × 20=2400
Probability =2400/55.440
=0.0432900433
Hence probability of selecting 3 females and 2 males is 0.04329
(Rounded to 5 decimals)
B) 4 females and 1 males
4 females selected from 6 female finalists in 6P4 ways
=6 × 5 × 4 ×3
=360
1 male selected from 5 male finalists in 5P1 ways
=5
Favourable ways =360 × 5=18000
Probability =1800/55.440
=0.0324675325
Hence probability of selecting 4 females and 1 male is 0.0324675
(Rounded to 7 decimals)
C) 5 females
5 females selected from 6 female finalists in 6P5 ways
=6 × 5 × 4 × 3 × 2
=720
Favourable ways = 720
Probability =720/55.440
=0.012987013
Hence probability of selecting 5 females is 0.012987
(Rounded to 6 decimals)
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