Rework problem 23 from section 2.4 of your text involving congressional committees. Assume that the committee consists of 6 Republicans and 5 Democrats. A subcommittee of 4 is randomly selected from all subcommittees of 4 which contain at least 1 Democrat. What is the probability that the new subcommittee will contain at least 2 Democrats?

Question

Mathematics

Hebert

12 May, 13:45

Rework problem 23 from section 2.4 of your text involving congressional committees. Assume that the committee consists of 6 Republicans and 5 Democrats. A subcommittee of 4 is randomly selected from all subcommittees of 4 which contain at least 1 Democrat. What is the probability that the new subcommittee will contain at least 2 Democrats?

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Answers (2)

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Devyn Chen · Answer 1

21/22 or 0.955 (3 sf)

43/66 or 0.652 (3 sf)

Step-by-step explanation:

P (atleast 1 Democrat)

= 1 - P (no Democrat)

= 1 - (6C4/11C4)

= 1 - 1/22 = 21/22 or 0.955 (3 sf)

P (atleast 2 Democrats)

= 1 - P (0 or 1 Democrats)

= 1 - 1/22 - (6C3*5C1) / 11C4

= 1 - 1/22 - 10/33

= 43/66 or 0.652 (3 sf)

Piper Wilson · Answer 2

21/22 or 0.955 (3 sf)

43/66 or 0.652 (3 sf)