Question 1115289: Find the conditional probability of the indicated event when two fair dice (one red and one green) are rolled.
The red one is 4, given that the sum is 9.
Found 2 solutions by rothauserc, ikleyn:
Answer by rothauserc(4718)   (Show Source):
You can put this solution on YOUR website! there are 36 events in the sample space
:
(r1, g1), (r1, g2), (r1, g3), (r1, g4), (r1, g5), (r1, g6)
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(r2, g1), (r2, g2), (r2, g3), (r2, g4), (r2, g5), (r2, g6)
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(r3, g1), (r3, g2), (r3, g3), (r3, g4), (r3, g5), (r3, g6)
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(r4, g1), (r4, g2), (r4, g3), (r4, g4), (r4, g5), (r4, g6)
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(r5, g1), (r5, g2), (r5, g3), (r5, g4), (r5, g5), (r5, g6)
:
(r6, g1), (r6, g2), (r6, g3), (r6, g4), (r6, g5), (r6, g6)
:
Note r means red die and g means green die
:
The problem asks for the probability that the red one is 4, given that the sum is 9
:
we can see that there is one event (r4, g5) that satisfies and the probability is 1/36
:
Answer by ikleyn(52916)  (Show Source):
You can put this solution on YOUR website! .
Given that the sum is 9, we have only 4 possible pairs
(r3,g6), (r4,g5), (r5,g4), (r6,g3).
It is the full space of events under given restriction.
Of them, only one pair (r4,g5) is red 4.
Hence, the conditional probability under the question is  .
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