Question

The chances of a team winning a match is 0.4. Find the probability that the team will win at least one match out of five.

Answer 1

The probability that the team will win at least one match out of five is 2882/3125=0.92224.

1. Probability of team winning is 0.4. And from compliment we can find the probability of team losing is 0.6.       [1-0.4]

2. We need to find probability that the team wins at least one out of five matches and for that we are going to use compliment again.

P(winning at least one of five matches)=1-P(winning none of the five matches)

P(X>=1)=1-P(X<1)

=1-P(X=0)

3. To find P(X=0). In elaborate the team should loose the first match simultaneously losing the second and so on which means the team should loose five times

P(X=0)=(0.6)⁵=0.07776.

4. So P(X>=1)=1-0.07776=0.92224

The probability that the team will win at least one match out of five is 0.92224