Probability

Question

A certain goalkeeper catches 30% of all penalty kicks against her team. What is the probability that out of 5 penalty kicks she catches 2? What is the probability that out of 5 penalty kicks she catches at least 2?

Answer 1

This is an example of binomial probability.  You have the five trials, each with a 30% chance of success and a 70% chance of failure.

 

The formula for binomial probably is:

 

P(x successes) = (_nC_x) · p^x · (1-p)^n-x

 

where p is the probability of success on any given trial.

 

Therefore,

P (2 success) = (₅C₂) · (.30)² · (1-.30)^5-2 = 10 · (.30)² · (.70)³ = 0.3087

 

Next, P (At least 2) = P(2 successes) + P(3 successes) + P(4 successes) + P(5 successes)

                             = (₅C₂) · (.30)² · (1-.30)^5-2 + (₅C₃) · (.30)³ · (1-.30)^5-3 + (₅C₄) · (.30)⁴ · (1-.30)^5-4 + (₅C₅) · (.30)⁵ · (1-.30)^5-5

                             = 10 · (.30)² · (.70)³ + 10 · (.30)³ · (.70)² + 5 · (.30)⁴ · (.70)¹ + 1 · (.30)⁵ · (.70)⁰

                             = 0.33003