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United States Congress - Case Study

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Case Study – United States Congress

ANSWERS:

#1

The probability that a randomly selected representative is female is: 77/432 = 0.178 Ans.

The probability that a randomly selected senator is female is: 20/100 = 0.20 Ans.

#2

There are 18% females in the House of Representatives in United States Congress, where as 20% females in the House of Senate. Relatively proportion of Males is more in the House of Representatives and less in the House of Senate.

#3 a.:

The probability that representative is Male is: 355/432 = 0.822 Ans.

#3 b.:

The probability that representative is Republican is: 232/432 = 0.537 Ans.

#3 c.:

The probability that representative is Male given that the Representative is a Republic is: 213/232 = 0.918 Ans.

#3 d.:

The probability that representative is female and Democrat is: 58/432 = 0.134 Ans.

#3 e.:

If the knowledge that some event B has occurred influences the probability of the occurrence of another event A, then A and B are said to be dependent events. If knowing that event B has occurred does not affect the probability of the occurrence of event A, then A and B are said to be independent events. Two events are independent if the following equation is satisfied. Otherwise the events are dependent.

P(A I B) = P(A)

Now in the House of Representatives, P (Female) = 77/432 = 0.178 and

P(Female|Democrat) = 58/200 = 0.29

Since P(Female|Democrat) P (Female), the events “being female” and “being a Democrat” are dependent events.

#4 a.:

The probability that senator is Male is: 80/100 = 0.80 Ans.

#4 b.:

The probability that senator is Not a Democrat is: (45+2)/100 = 0.47 Ans.

#4 c.:

The probability that senator is Female or a Republic is: (20/100) + (45/100) – (4/100) =.2+0.45-0.04 = 0.61 Ans.

#4 d.:

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