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red ball

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by maihuna » Sat Aug 15, 2009 12:28 am
An urn contains 5 red and 5 black balls. A ball is drawn at random, its colour is noted and is returned to the urn. Moreover, 2 additional balls of the colour drawn are put in the urn and then a ball is drawn at random. What is the probability that the second ball is red?
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Re: red ball

by dtweah » Sat Aug 15, 2009 3:26 am
maihuna wrote:An urn contains 5 red and 5 black balls. A ball is drawn at random, its colour is noted and is returned to the urn. Moreover, 2 additional balls of the colour drawn are put in the urn and then a ball is drawn at random. What is the probability that the second ball is red?
Let S be the event that second ball is Red

First ball could be Red or Black. So form a partition of sample space.

Let R be event first ball is Red and B be event first ball is Black

Then by law of total probability


P(S)= P(S|R)P(R) + P(S|B)P(B)

= 7/12 x 1/2 + 5/12 x 1/2 = 1/2
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by prindaroy » Sat Aug 15, 2009 9:17 pm
[5/10*7/12]/[(5/10*7/12)+(5/10*7/12)] = 1/2
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