Three Toronto Maple Leaf fans attend a Flames-Leafs game in the Saddledome. The

Question

Three Toronto Maple Leaf fans attend a Flames-Leafs game in the Saddledome. The probability that the first fan will wear their "Leafs jersey is 0.75. The probability that the second fan will wear their "Leafs" jersey is 0.69. The probability that the third fan will not wear their "Leafs" jersey is 0.75. Let X be a random variable which measures how many of the three Leaf fans mentioned are wearing their "Leafs" jersey to this hockey game Assuming that each "Leaf fan mentioned wears their "Leaf jersey independently of each other, find the probability distribution of X. P(X = 0) = P(x = 1) = P(x = 2) = P(x = 3) = Put answers in four decimal places.

Explanation / Answer

We are given that

p1=0.75 , p2=0.69 and p3=1-0.75= 0.25 are the probabilities of wearing the jersey. Then

the distrbution can be calculated as

P(X=0)=(1p1)(1p2)(1p3)P(X=0)=(1p1)(1p2)(1p3) = (1-0.75)*(1-0.69)*(1-0.25) = 0.058

P(X=1)=p1(1p2)(1p3)+(1p1)p2(1p3)+(1p1)(1p2)p3

0.75*(1-0.69)*(1-0.25) +(1-0.75)*(1-0.25)*0.69 + 0.25*(1-0.69)*0.75 = 0.361

P(X=2)=p1p2(1p3)+p1(1p2)p3+(1p1)p2p3

0.75*0.69*(1-0.25) + 0.75*(1-0.69)*0.25 + (1-0.75)*0.69*0.25= 0.489

P(X=3)=p1p2p3 = 0.75*0.69*0.25= 0.129

Hope this helps

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