The ski lift at Thunder Mountain called Devils Canyon is quite dangerous. Usually 2% of the skiers who attempt the run will injure themselves due to falls.

8. What is the probability that exactly 3 of the next 100 skiers who attempt this run will injure themselves?

Answer Choices:

0.126

0.175

0.182

0.215

This problem involves a Bernoulli trial with the binomial distribution.

p = 2% = 0.02, the probability of injury

q = 1 - p = 0.98, the probability of no injury.

n = 100, the number of trials (skiers)

r = 3, expected number of injuries

The probability of 3 injuries is

P (3 of 100) = ₁₀₀C₃ p³q ⁽¹⁰⁰⁻³)

= 161700 * (0.02³) * (0.98⁹⁷)

= 0.1823

Answer: 0.182