Question

The Wildcats and the Leopards are evenly matched football teams. Whenthey play, there is a 0.5 probability that the Wildcats will win. If they play 9times, what is the probability that the Wildcats will win 6 of the games?Round your answer to the nearest tenth of a percent.A 24.6%B. 0.2%O C. 7.0%D. 16.4%

Answer 1

To answer this question, we need to use the probability using the Binomial Distribution. Because we are finding an exact probability, we can use the next formula:

`C(9,6)\cdot((1)/(2))^6\cdot((1)/(2))^((6-3))=0.1640`

Or the probability is about 16.40%.

C(9, 6) is the combination of 9 out of 6. They are going to play 9 games, but we are finding the probability that the Wildcats win 6. Then:

`C(n,k)=(n!)/((n-k)!\cdot k!)\Rightarrow C(9,6)=(9!)/((9-6)!\cdot6!)=(9\cdot8\cdot7\cdot6!)/(3!\cdot6!)=(9\cdot8\cdot7)/(3\cdot2\cdot1)=84`

Then, the general formula for the Binomial Distribution is:

`C(n,k)\cdot(p)^k\cdot(q)^(n-k)`

In this case, the probability of p = q = 1/2, k = 6, n = 9. Then, applying the formula, we obtain a probability of 0.1640 or about 16.40%. The correct option is D.