The probability that a football game will go into overtime is 10% what is the probability that exactly two ofthree football games will go to into overtime?

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Answer 1 · 2018-06-19T05:24:28

# 0.027#.

Let us call going overtime of a football game a success.

Then, the probability (prob.) #p# of success is #p=10%=1/10#, so

that, the prob. #q# of failure is #q=1-p=9/10#.

If, #X=x# denotes the number of football games that go overtime,

then, #X=x# is a Binomial Random Variable with parameters

#n=3, p=1/10, &, q=9/10, i.e., X~B(3,1/10)#.

#:."The Reqd. Prob."=P(X=2)=p(2)#.

We have, for #X~B(n,p),#

#P(X=x)=p(x)=""_nC_xp^xq^(n-x), x=0,1,2,...,n#.

#:."The Reqd. Prob."= P(X=2)=p(2)=""_3C_2(1/10)^2(9/10)^1#,

#=3*1/100*9/10#.

#=0.027#.