8. 44 P 023 Senators: Suppose the following are data for the 100 Senators from t

Question

8. 44 P 023 Senators: Suppose the following are data for the 100 Senators from the Congress of the United States. Male Female Republican Democrat Independent 39 10 43 Find the requested probabilities. Round your answers to 3 significant digits". (a) If two different senators are randomly selected, what is the probability that they are both male republicans? P(male republican and male republican)- (b) If two different senators are randomly selected, what is the probability that the first is a democrat and the second is a republican? Ademocrat and republican)-E 0242 (c) If two different senators are randomly selected, what is the probability that they are both female democrats? P(female democrat and female democrat)· (d) If two different senators are randomly selected, what is the probability that the first is a female and the second is a male? P(female and male)- 100136 ) ) X Significant Digits: Here are some probablities expressed to 3 significant digits. You start counting digits from left to right starting with the first non-zero 0.123 0.0123 0.0120 o.00123 0.102 o.aso Additional Materials

Explanation / Answer

b) Probability that first is a democrat=(39+10)c1/100c1

Proability that second is a republican=(43+6)c1/99c1

probability that first is a democrat and second is a republican=(49/100)*(49/99)=0.242

d) probability that first is a female =(6+10+0)c1/100c1

probability that second is a male=(43+39+2)c1/99c1

probability that first is a female and second is a male=(16/100)*(84/99)=0.136

a)probability that they are both male republicans =p(M and R)=p(M)*p(R)

(since both are independent events)

p(M)=43/84

p(R)=43/49

p(MandR)=(43*43)/(84*49)=0.449

c) probability that they are both female democrats=p(FandD)=p(F)*p(D)

(since both are independent events)

p(F)=10/16

p(D)=10/49

p(F)*p(D)=(10*10)/(16*49)=0.127

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