Two basketball players throw a ball into the basket till the first hit.

The probability for the first player tol hit the target is 5%, but for the second - 15%.

What is the partition law for the number of attempts both player made.

thanks for help.

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- Apr 11th 2013, 12:48 PMKiieferspartition law
Two basketball players throw a ball into the basket till the first hit.

The probability for the first player tol hit the target is 5%, but for the second - 15%.

What is the partition law for the number of attempts both player made.

thanks for help. - Apr 11th 2013, 01:41 PMHallsofIvyRe: partition law
Are you asking "how can I look at this problem and immediately know the aswer without doing any calculation?" I have no idea. But sitting down and doing some calculations might well show a pattern.

The first player will win on the first throw .05 of the time.

The second player will win on his first throw if the first player misses and he hits: (.95)(.15)

The first player will win on the second throw if the first player misses on the first try, second player misses, first player hits on second try: [tex](.95)(.85)(.05)

The second player will win on his second throw if the first player misses, second player misses, first player misses, second player hits: [tex](.95)(.85)(.95)(.15)

The first player will win on the third throw if they both miss twice and the he hits: (.95)(.85)(95)(.85)(.05)

The second player will win on the third throwif they bothiss twice, the first player misses, the second player hits: (.95)(.85)(.95)(.85)(.95)(.15)

So far for the first player we have

1: .05= ((.95)(.05))^0(.05)

2: .95(.85)(.05)= ((.95)(.85)^1)(.05)

3: .95(.85)(.95)(.85)(.05)= ((.95)(.85))^2(.05)

See a pattern? - Apr 13th 2013, 11:19 AMKiiefersRe: partition law