Unit 11 Test Probability & Statistics

Question

The odds of winning a game at the carnival are 3 in 7. If Liza plays the game nine times, what is the probability that she wins exactly two times?

Answer 1

Hi Ian.

This is a binomial probability distribution problem and can be solved using a calculator with a binompdf feature (TI-83/84 for sure) or using the following formula: C(n, x) • p^x • q^n-x

n is the number of trials; n = 9 (Liza plays 9 times)

x is the number of successes; x = 2 (If she wins exactly 2 times)

p is the probability of success; p = 3/7 or approx 0.43 (odds of winning ratio)

q is the probability of failure; q = 4/7 or approx 0.57 (odds of losing ratio)

Therefore it would be C(9, 2) • (3/7)² • (4/7)^9-2 which equals approx 13%.

I hope this helps you understand the concept so you can do more problems like this.

Sincerely,

Shaniqua