Probability of saving goals

Question

A goalkeeper catches 30% of all penalty kicks against her team.

a. What is the probability that out of 5 penalty kicks she catches 2?

b. What is the probability that out of 5 penalty kicks she catches 2 or more?

Answer 1

(a)

Success rate of goalkeeper is 30% = 0.30.

Find the probability that out of 5 penalty kicks she catches 2.

Let  be the event that the goalkeeper catches 2 out of 5 penalty kicks.

The probability for k successes is .

Where n is number of samples(trails),

           p is probability of success,

          q  is probability of failure.

Probability that out of 5 penalty kicks she catches 2 is .

Probability that out of 5 penalty kicks she catches 2 is 0.3087.

Answer 2

(b)

Success rate of goalkeeper is 30% = 0.30.

Find the probability that out of 5 penalty kicks she catches 2 or more.

Let  be the event that the goalkeeper catches 2 or more out of 5 penalty kicks.

The probability for k successes is .

Where n is number of samples(trails),

           p is probability of success,

          q  is probability of failure.

Probability that out of 5 penalty kicks she catches 2 or more is .

Property of probability: .

Hence .

Probability that out of 5 penalty kicks she catches 2 or more is 0.47.