(1 point) Three Toronto Maple Leaf fans attend a Flames-Leafs game in the Saddle

Question

(1 point) 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 0.61. The probability that the second fan will wear their "Leafs" jersey is 0.85. The probability that t 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. he third fan will not wear their "Leafs" jersey is 0.82. Let X be a random variable which P(X = 1) = P(X = 2) = P(X = 3) = Put answers in four decimal places.

Explanation / Answer

Fans are independent of each other

X= 0 , no fan wears jersey

Prob = 0.39 * 0.15* 0.82 = 0.0480

X = 1, only one fan wears jersey

Prob = 0.61*0.15*0.82+0.85*0.39*0.82 + 0.18*0.39*0.15 = 0.07503+0.27183+0.01053= 0.3574

X =2, any two wears Jersy

Prob = 0.61*0.85*0.82 +0.61*0.15*0.18+0.39*0.85*0.18 = 0.42517+0.01647+0.05967 = 0.5013

X= 3, all three wears jersey

Prob = 0.61*0.85*0.18 = 0.0933

Fan With Jersey Without Jersey 1st 0.61 0.39 2nd 0.85 0.15 3rd 0.18 0.82

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