Three Toronto Maple Lear fans attend a Flames-Leafs game in the saddledome. The

Question

Three Toronto Maple Lear fans attend a Flames-Leafs game in the saddledome. The probability that the first fan will wear their "Leafs" jersey is 0.63. The probability that the second ran will wear their "Leafs" jersey is 0.55. The probability that the third fan will not wear their "Leafs" jersey is 0.9. 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 " fan mentioned wears their "Leaf" jersey independently of each other, find the probability distribution of X. P(X =0) = 1 P(X = 1) = P(X = 2) = 0.2587 P(X = 2) = 0.5358 P(X = 3) = 0.1663

Explanation / Answer

For X=0, neither of the fans wear their jersey, for X=1, one can assume that the first fan wears jersey, followed by the other two fans non wearing it. Then second fan wearing jersey, the first and third fans are not wearning it, and lastly the the third fan wears it, when first and second are not allowed to wear it.

For X=2, assume first and second fan wear jersey, and thirs is not wearing, then first and third fans are wearing it, whereas, second one is not wearing it, lastly second and third fans were wearing it, wheras, first one is not wearing it.

For X=3, all three fans are wearing it.

The probability distribution of the random variable, X is as follows:

X P(X) 0 0.37*0.45*0.9=0.1499 1 0.63*0.45*0.9+0.37*0.55*0.9+0.1*0.37*0.45=0.4550 2 0.63*0.55*0.9+0.63*0.1*0.45+0.55*0.1*0.37=0.3606 3 0.63*0.55*0.1=0.0347

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