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be the event that the goalkeeper catches 2 out of 5 penalty kicks. \ \
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.
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A goalkeeper catches 30% of all penalty kicks.
\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. \ \
Success rate of goalkeeper is 30% = 0.30.
\The probability for k successes is ![\"\"](\"http://www.mathskey.com/test/fckeditor/editor/plugins/fckeditor_wiris/integration/showimage.php?formula=425cf0c8a2933b2c0ef7d9c218c8d92d.png\")
.
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 ![\"\"](\"/test/fckeditor/editor/plugins/fckeditor_wiris/integration/showimage.php?formula=36fbf5471397cf633b9b022d0c047a0f.png\")
.
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Probability that out of 5 penalty kicks she catches 2 is 0.3087.
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\
\
(b)
\Success rate of goalkeeper is 30% = 0.30.
\Find the probability that out of 5 penalty kicks she catches 2 or more.
\Let ![\"\"](\"/test/fckeditor/editor/plugins/fckeditor_wiris/integration/showimage.php?formula=29d33e6e543cb2642c14476b4d183256.png\")
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 ![\"\"](\"/test/fckeditor/editor/plugins/fckeditor_wiris/integration/showimage.php?formula=cd0c69ac8b2491f830c22c7bb75d83e9.png\")
.
Property of probability: ![\"\"](\"/test/fckeditor/editor/plugins/fckeditor_wiris/integration/showimage.php?formula=f4153ba1eadde9baa34104e7ce804804.png\")
.
Hence ![\"\"](\"/test/fckeditor/editor/plugins/fckeditor_wiris/integration/showimage.php?formula=62a8b4eb7116da231e938f49fa76c300.png\")
.
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![\"\"](\"/test/fckeditor/editor/plugins/fckeditor_wiris/integration/showimage.php?formula=5623ac7fdb0568453508f0b217ec163c.png\")
Probability that out of 5 penalty kicks she catches 2 or more is 0.47.
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