Jeff is a sports fan. He has a wish list to see a 1. baseball, 2. basketball, an

Question

Jeff is a sports fan. He has a wish list to see a 1. baseball, 2. basketball, and 3. football game this year. Two of his friends independently deicde to buy him tickets to one event. John has a probability of selecting tickets to 1,2, and 3 with a probability 1/5, 2/5, and 2/5. Jason has a probability of selecting tickets to 1, 2, and 3, respectively with probability 4/7, 1/7, 2/7, respectively. What is the probability John and Jason give Jeff a ticket to a different type of sporting event? Given the tickets are to different sporting events, what is the probability the event is baseball?

Explanation / Answer

a) probability John and Jason give Jeff a ticket to a different type of sporting event

=P(john give for 1 and Jason for 2+john give for 1 and Jason for 3+john give for 2 and Jason for 1+john give for 2 and Jason for 3+john give for 3 and Jason for 1+john give for 3 and Jason for 2)

=(1/5)*(1/7)+(1/5)*(2/7)+(2/5)*(4/7)+(2/5)*(2/7)+(2/5)*(4/7)+(2/5)*(1/7)=5/7

b) probability the event is baseball given tickets are to different sporting events

=P(ohn give for 1 and Jason for 2+john give for 2 and Jason for 1+john give for 3 and Jason for 1)/P( difffernt tickets) =((1/5)*(1/7)+(1/5)*(2/7)+(2/5)*(4/7)+(2/5)*(4/7))/(5/7)

=19/25

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