Question

A basketball team will play a 44-game season. Twenty-six of these games are against class A teams and 18 are against class B teams. Suppose that the team will win each game against a class A team with probability 0.4 and will win each game against a class B team with probability 0.7. Suppose also that the results of the different games are independent.

Approximate the probability that the team wins 25 games or more?

0.3278

           
0.33

           
0.31

           
0.3178

Answer 1

here expected number of games won =26*0.4+18*0.7 =23

and standard deviation =sqrt(Var(A)+Var(B))=sqrt(26*0.4*0.6+18*0.7*0.3)=3.165

from normal approximation:

probability that the team wins 25 games or more

probability =P(X>24.5)=P(Z>(24.5-23)/3.165)=P(Z>0.47)=1-P(Z<0.47)=1-0.6822=0.3178