Question

NEED HELP! 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

We will be using the binomial probability formula to solve the problem

The formula is given by ⁿCₓ (p)ˣ (1-p)ⁿ⁻ˣ

Where:
n = the number of trials = 100
x = the number of samples we are trying on = 3
p = the probability of success = 2% = 0.02

We can either calculate ⁿCₓ by using the scientific calculator using the $^nC_r$ button or by doing it manually use $\frac{n!}{(n-x)!x!}$

P(3) = ¹⁰⁰C₃ (0.02)³ (1 - 0.02)¹⁰⁰⁻³
P(3) = ¹⁰⁰C₃ (0.02)³ (0.98)⁹⁸
P(3) = 0.182 (rounded to three decimal places)

Correct answer: option 3