Question

An executive committee consists of 13 ​members: 5 men and 8 women. 4 members are selected at random to attend a meeting in Hawaii. The names are drawn from a hat. What is the probability that all 4 selected are men​?

Answer 1

0.0069 (method 1) ; 0.0067 (method 2)

Explanation:

Probability is calculating the likelihood of an event.

Probability (4 members chosen out of 5 men & 8 women, are all men ):

[ 5C4 x 8C0 ] / [ 13C4]

= [ (5! / 4!) x (1) ]

[ 13! (4! . 9!) ]

5 / 715 = 0.0069

• Alternative method

Probability of choosing 1st man = 5/13

Probability of choosing 2nd man = 4/12

Probability of choosing 3rd man = 3/11

Probability of choosing 4th man = 2/ 10

5/13 x 4/12 x 3/11 x 2/10

0.38 x 0.33 x 0.27 x 0.2

= 0.0067

Answer 2

The probability that all 4 selected are men committee consists of 13 members

`P(E) = (1)/(143)`

Explanation:

Step:1

An executive committee consists of 13 ​members

men + women = 5 +8 =13

A committee consists of 4 men's out of 13 ​members can be formed in 'n'

=
`13c_(4) ways`

= 715

Let 'E' be the event of selecting men

m = n(E) =
`5c_(4) ways` = 5

The probability that all 4 selected are men committee consists of 13 members

`P(E) = (n(E))/(n(S))`

`P(E) = (5)/(715)`

`P(E) = (1)/(143)`