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Probability of saving goals

0 votes
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?
asked Oct 17, 2015 in PRECALCULUS by egbush Rookie

2 Answers

0 votes

(a)

Success rate of goalkeeper is 30% = 0.30.

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

Let image 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 image.

image

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

answered Oct 17, 2015 by Lucy Mentor
edited Oct 17, 2015 by Lucy
0 votes

(b)

Success rate of goalkeeper is 30% = 0.30.

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

Let image 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 image.

Property of probability: image.

Hence image.

image

image

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

answered Oct 17, 2015 by cameron Mentor

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