The city council of a particular city is composed of five me

The city council of a particular city is composed of five members of party A, four members of party B, and three independents. Two council members are randomly selected to form an investigative committee.

A Find the probability that both are from party A.

B Find the probability that at least one is an independent.

C Find the probability that the two have different party affiliations (that is, not both A, not both B, and not both independent).

Solution

A.

There are 12 members here.

Thus, there are 12C2 = 66 possible options.

There are 5C2 = 10 ways to choose from party A.

hence

P(both A) = 10/66 = 0.151515152 [ANSWER]

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B.

P(at least one ind) = 1 - P(no independent)

There are 9 non-independents here.

Hence, there are 9C2 = 36 ways to choose.

Thus,

P(no independent) =36/66= 0.545454545

Therefore,

P(at least one ind) = 1 - 0.545454545

= 0.454545455 [ANSWER]

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c)

There are 3 possibilities:

1A, 1B: 5*4 = 20 ways
1B, 1C: 4*3 = 12 ways
1A, 1C: 5*3 = 15 ways

Hence, there\'s a total of 47 ways.

hence

P(different) = 47/66 = 0.712121212 [ANSWER]