1. 110 points My A committee has 7 members. There are 4 men and 3 women are on a
ID: 3338715 • Letter: 1
Question
1. 110 points My A committee has 7 members. There are 4 men and 3 women are on a committee. Beth is one of the women. Two of the 7 people are randomly chosen to serve as officers. Answer the following questions.(Give your answers correct to three decimal places.) (a) What is the probability that both officers will be women? (b) What is the probability at least one officer will be a woman? c)If you know that at least one of the officers is a woman, what is the conditional probability that both officers will be women? (d) If you know that Beth is one of the officers, what is the conditional probability that both officers are women?Explanation / Answer
Solution :
Given ,
totel members in a commettee = 7
number of men in the commettee = 4
number of women in the commettee = 3
And beth is one of the women
two members are selected randomly to serve as officers
( a )
the probability that both officers be women = 3c2 / 7c2 = 3 / 21 = 0.1428
( b )
the probability of at least one officer will be women = 1 - ( probability that none of the officers will be women)
= 1 - ( 4c2 / 7c2 )
= 1 - 0.2857
= 0.7142
( c )
number of ways that atleast one of the officers is a woman = ( 3 * 4 ) + 3c2 = 15
number of ways that both officers are women = 3c2 = 3
the probability that both are women whem given atleast one officers is a woman = 3 / 15 = 1 / 5 = 0.200
( d )
probability tha both are women when we know that one of them is beth = 2c1 / 6c1 = 2 / 6 = 0.3333
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