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 0.59. The probability that the second fan will wear their "Leafs" jersey is 0.88. The probability that the third fan will not wear their "Leafs" jersey is 0.53. 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.

(=0)=

(=1)=

(=2)=

(=3)=

Put answers in four decimal places.

Explanation / Answer

(=0)= P(none wear )=(1-0.59)*(1-0.88)*0.53=0.0261

P(X=1)=P(first wear and rest do not )+P(secnd wear and rest not)+P(third wear and rest not)

=0.59*(1-0.88)*0.53+(1-0.59)*0.88*0.53+(1-0.59)*(1-0.88)*(1-0.53)=0.2519

P(X=2)=P(first 2 waer and third not )+P(first and third but nt 2nd)+P(first not but 2nd and 3rd)

=0.59*0.88*0.53+0.59*(1-0.88)*(1-0.53)+(1-0.59)*0.88*(1-0.53)=0.4780

P(X=3)=P(all 3 wears) =0.59*0.88*(1-0.53)=0.2440

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.