There are 5 women and 3 men waiting on standby for a flight to New York.

Ava-May Nelson

Ava-May Nelson

Answered question

2021-06-25

There are 5 women and 3 men waiting on standby for a flight to New York. Suppose 3 of these 8 people are selected at random, and a random variable X is defined to be the number of women selected. Find Pr[X=2].

Answer & Explanation

liannemdh

liannemdh

Skilled2021-06-26Added 106 answers

We need to select 3 of the 8 people. Since the order of the people is not important (as a different order results in the same people being selected), we need to use a combination.
Definition combination (order is not important);nCr=(nr)=n!r!(nr)! with n!=n(n1)21. # of possible outcomes=sC3=8!3!(83)!=8!3!5!=56
We need to select 2 of the 5 women and 1 of the 3 men to obtain X=2. # of favorable outcomes=(5C23)C1=(5!2!3!)3!1!2!=103=30
The probability is the number of favorable outcomes divided by the number of possible outcomes: Pr(X=2)=# of favorable outcomes # of possible outcomes =3056=1528  0.5357=53.57%

Ian Adams

Ian Adams

Skilled2021-08-04Added 163 answers

We need to select 3 of the 8 people. Since the order of the people is not important (as a different order results in the same people being selected), we need to use a combination.
Definition combination (order is not important);nCr=(nr)=n!r!(nr)! with nn(n1)21. # of possible outcomes=sC3=8!3!(83)!=8!3!556
We need to select 2 of the 5 women and 1 of the 3 men to obtain X=2. # of favorable outcomes=(5C23)C1=(5!2!3!)3!1!2103=30
The probability is the number of favorable outcomes divided by the number of possible outcomes: # of favorable outcomes # of possible outcomes =30/56=15/28=0.5357=53.57

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