7 ater 4: Problen Set 60 23. Senators: Use the following data for the 100 Senato

Question

7 ater 4: Problen Set 60 23. Senators: Use the following data for the 100 Senators from the 112th Congress of the United States Republican Democrat Independent 39 12 Male End 42 Female 0 (a)" If two different senators are randomly selected, what is the probability that they are both male (b)" If two different senators are randomly selected, what is the probability that the first is a democrat (c) If two different senators are randomly selected, what is the probability that they are both female (d) If two different senators are randomly selected, what is the probability that the first is a female republicans? and the second is a republican? democrats? and the second is a male? One Bad Apple - Probabilities of At Least One (4.5) nt of ell snark-nlugs are defective

Explanation / Answer

Fist if we find row total and column total, we get

a)P(both male republican)=P(1st male republican)*P(2nd male republican)

=(42/100)*(41/99)=0.1739

b)Required probability =P(1st democrant)*P(2nd is republican)

=(51/100)*(47/99)=0.2421

c)P(both female democrats)= P(1st female democrats)*P(2nd female democrats)

=(12/100)*(11/99)=0.0133

d)Required Probability =P(1st is a female)*P(2nd is a male)

=(17/100)*(83/99)=0.1425

Republican Democrat Independent Total Male 42 39 2 83 Female 5 12 0 17 Total 47 51 2 100

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