Problem Set 9 3/5 9/60 3/4 6/60 3/5 2/5 3 3/5 18/60 3/4 penny 3/5B 6/60 nickel 4/60 quarter rob (d) What is the probability that an odd number of coins come up heads? Solution The probability of an event is the sum of the probabilities of the outcomes t. In this Pr(odd number of heads Pr({(H,H,H),(H,T,T),(T,H,T),(T,T,H)} Pr((h, H, H))+Pr(H,T,T))+ Pr((T,H, T))+ Pr(T,T, H)) 92126 Problem 2. Professor Plum, Mr. Green, and Miss Scarlet are all plotting to shoot Colonel Mustard. If one of these three has both an opportunity and the revolver then that person shoots Colonel Mustard. Otherwise, Colonel Mustard escapes. Exactly one of the three has an opportunity with the following probabilities Pr(Plum has opportunity)=1/6 Pr(Green has opportunity)=2/6 Pr( Scarlet has opportunity)=3/ 6 Exactly one has the revolver with the following probabilities, regardless of who has an opportunit revolver)=4/8 Pr(Green has revolver)=3 /8 Pr(Scarlet has revolver)=1/82 Problem Set 9 ❳❳❳ ❳❳❳ ✘✘✘ ✘✘✘ ❳❳ ❳❳❳ ❳ ✘✘ ✘✘✘ ✘ ❳❳ ❳❳❳ ❳ ✘✘ ✘✘✘ ✘ ❳❳❳ ❳❳❳ ✘✘✘ ✘✘✘ ❍❍ ❍ ❍❍ ❍ ✟✟ ✟✟ ✟✟ ❍ ❍❍ ❍ ❍❍ ✟✟ ✟✟ ✟✟ ❅ ❅ ❅ ❅ ❅ ❅ ￾ ￾ ￾ ￾ ￾ ￾ H T H T H T T H T H T H T H penny nickel quarter odd? × × × × prob. 1/3 2/3 3/4 1/4 3/4 1/4 3/5 2/5 3/5 2/5 3/5 2/5 3/5 2/5 9/60 6/60 3/60 2/60 18/60 12/60 6/60 4/60 (d) What is the probability that an odd number of coins come up heads? Solution. The probability of an event is the sum of the probabilities of the outcomes in that event. In this case: Pr (odd number of heads) = Pr ({(H, H, H),(H, T, T),(T, H, T),(T, T, H)}) = Pr ((H, H, H)) + Pr ((H, T, T)) + Pr ((T, H, T)) + Pr ((T, T, H)) = 9 60 + 2 60 + 12 60 + 6 60 = 29 60 Problem 2. Professor Plum, Mr. Green, and Miss Scarlet are all plotting to shoot Colonel Mustard. If one of these three has both an opportunity and the revolver, then that person shoots Colonel Mustard. Otherwise, Colonel Mustard escapes. Exactly one of the three has an opportunity with the following probabilities: Pr (Plum has opportunity) = 1/6 Pr (Green has opportunity) = 2/6 Pr (Scarlet has opportunity) = 3/6 Exactly one has the revolver with the following probabilities, regardless of who has an opportuntity: Pr (Plum has revolver) = 4/8 Pr (Green has revolver) = 3/8 Pr (Scarlet has revolver) = 1/8