A group of 4 neighbors has decided to form a bowling team. For various reasons t

Question

A group of 4 neighbors has decided to form a bowling team. For various reasons they believe that the probability that any given one of them shows up to bowl is 0.9, i.e. each is 90% reliable. The league requires teams to have 4 members present in order to bowl. Also, the league will not allow a team to bowl next year unless they have enough bowlers 70% or more of the 10 nights of bowling.

a. What is the probability the team has enough show up to bowl on a given night?

b. What is the probability that the team is not allowed to bowl next year?

c. The group is considering adding two more neighbors to the team. Assuming their attendance is more or less the same as the others, what is the probability the team has enough show up to bowl on a given night?

Explanation / Answer

a) P( team has shown up ) = P( 4 people show up)=0.9^4=0.6561

p=0.6561 q =1-0.6561= 0.3439

b) P( Team bowl next year) = 10C7 p^7 * q^3+ 10C8 p^8 * q^2+10C9 p^9 * q^1+ 10C10 p^10 q^0 = 0.53042526791

c) P( 4 or 5 or 6) = 6C4 * 0.9^4*0.1^2+6C5*0.9^5*0.1+6C6 * 0.9^6 = 15 * 0.9^4*0.1^2+6*0.9^5*0.1+1 * 0.9^6 = 0.98415

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