The following table is made up of serving members of the US House of Representat

Question

The following table is made up of serving members of the US House of Representatives from Caltlornia, showing their party atliations homeCYCrieie m LaMalfa is the probablity of choosing a committee of six made up of equal number of Democrats and Republicans? b. If a committee of 7 is to be chosen, made up of 4 Democrats and 3 Republicans, what is the chance that Pelosi is chosen? c. What is the probability of choosing a committee of 7, made up of 4 Democrats and 3 Republicans, i Nunes and Pelosi must be in the committee? (aNumber (b Number (c Number PRINT FACESHEET & INS CARD FOR NT Address Phone Numbers: Home, Work Mobile Preferred Number v' Email Address Race

Explanation / Answer

a) 8 democratic and 8 republic
Probability of both in equal number
= 8C3 * 8C3 / 16C6
= 56 *56/ 8008
= 0.39160839

b)total number of ways to choose 4 democrates and 3 republicans
= 8C4 * 8C3
number of ways that Pelosi is chosen
= 7C3 * 8C3
hence
required probability = 7C3 * 8C3 / (8C4 * 8C3)
= 7C3 / 8C4
= 35/70
= 0.5

c)
similar to b) part
7C3 * 7C2 / (8C4 * 8C3)
= 35 *21 /(70 * 56)
= 0.1875

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