SOLUTION: A city council consists of 7 males and 4 females. Two counsilors are selected at random to represent the city at an Elton John concert. what is the probability that A. both coun

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Question 253039: A city council consists of 7 males and 4 females. Two counsilors are selected at random to represent the city at an Elton John concert. what is the probability that
A. both councilors are male?
B. one councilor is a male and one a female?
C. at least one councilor is a female?

Answer by palanisamy(496) (Show Source):
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A city council consists of 7 males and 4 females.
Total number of counsilors = 7+4 = 11
Two counsilors are selected at random
Total number of ways of forming the committee= 11C2
= 11*10/2
=55
A) If both counsilors are males
Out of 7 males 2 can be selected in 7C2 ways
Number of favourable events = 7*6/2 = 21
Probability p(A) = 21/55
B)one councilor is a male and one a female
Out of 7 males 1 can be selected in 7 ways and out of 4 females 1 can be selected in 4 ways.
Number of favourable events = 7*4 = 28
Probability p(B) = 28/55
C). At least one councilor is a female
There are two possibilities.
one male and one female or 2 females.
In the first case probability = 28/55 ...(1)
In the second case, out of 4 females 2 can be selected in 4C2 ways.
Number of favourable events = 4*3/2 = 6
Probability = 6/55 ...(2)
The required probability that at least one councilor
is a female = (28/55)+(6/55)
= 34/55