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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​?

User Tim Lesher
by
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2 Answers

0 votes

Answer:

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

User Starpause
by
8.1k points
6 votes

Answer:

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)

User Wstr
by
7.6k points

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