You and your friend Anderson both take the bus home after class. Every Monday, W

Question

You and your friend Anderson both take the bus home after class. Every Monday, Wednesday and Friday, you and Anderson will take one of the 5:10 p.m., 5:15 p.m., or 5:20 p.m. buses. You are equally likely to take any of the three buses. Anderson is more likely to take the 5:10 p.m. bus (with probability 1/2) than 5:15 p.m. and 5:20 p.m. bus (with probability 1/4 each). Assume that the bus rides are independent from each other. a) What is the probability that you and Anderson will have attended no more than 3 lectures before you both take the same bus home for the first time? b) What is the expected number of lectures you and Anderson will have attended until you both take the same bus home for the third time? Find the variance as well.

Explanation / Answer

probabilty that you and anderson both will take same bus =P(both take 5:10 bus+5.:15 bus+5:20 bus)

=(1/3)*(1/2)+(1/3)*(!/4)+(1/3)*(1/4)=1/3

a) probabilty that you take same bus for at most 3 lectures =P(on first lecture+not on first on second lecture+not on first 2 and on 3rd lecture) =(1/3)+(2/3)*(1/3)+(2/3)2*(1/3)=0.7037

b) expected number of bus =r/p=3/(1/3)=9

variance =r*(1-p)/p2=3*(1-1/3)/(1/3)2 =18

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