Question

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

Answer 1

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