Anish Buchanan

2021-03-07

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

(1) 3 females and 2 males?

(2) 4 females and 1 male?

(3) 5 females?

un4t5o4v

Skilled2021-03-08Added 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 calculate the probability of selecting an item as described below.

The total number of ways:

Total number of ways of selecting 5 people from 11 finalists is given by,

$11P5$

$=11\text{}\times \text{}10\text{}\times \text{}9\text{}\times \text{}8\text{}\times 7$

$=55.440$

Probability is given by the ratio of number of favourable ways to the total number of ways.

Note :

$nPr=n\text{}\frac{!}{n\text{}-\text{}r}!$

1) 3 females and 2 males

3 females selected from 6 female finalists in $6P3$ ways

$=6\text{}\times \text{}5\text{}\times 4$

$=120$

2 males selected from 5 male finalists in $5P2$ ways

$=5\text{}\times \text{}4$

$=20$

Favourable ways $=120\text{}\times \text{}20=2400$

Probability $=2400/55.440$

$=0.0432900433$

The probability of selecting 3 females and 2 males is 0.04329

(Rounded to 5 decimals)

2) 4 females and 1 males

4 females selected from 6 female finalists in $6P4$ ways

$=6\text{}\times \text{}5\text{}\times \text{}4\text{}\times 3$

$=360$

1 male selected from 5 male finalists in $5P1$ ways

$=5$

Favourable ways $=360\text{}\times \text{}5=18000$

Probability $=1800/55.440$

$=0.0324675325$

The probability of selecting 4 females and 1 male is 0.0324675

(Rounded to 7 decimals)

3) 5 females

5 females selected from 6 female finalists in $6P5$ ways

$=6\text{}\times \text{}5\text{}\times \text{}4\text{}\times \text{}3\text{}\times \text{}2$

$=720$

Favourable ways = 720

Probability $=720/55.440$

$=0.012987013$

The probability of selecting 5 females is 0.012987

(Rounded to 6 decimals)

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