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Question
A black and a red dice are rolled.
Find the conditional probability of obtaining the sum 8, given that the red die resulted in a number less than 4.
Solution
The sum of the reserves on the E event dice is assumed to be 8, and the number shown on the F event red die has a compatibility of less than 4.
E = {(2, 6), (3, 5), (4, 4), (5, 3), (6, 2)}
F = {(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6)}
Total types = 18
E ∩ F = {(2, 6), (3, 5)}
P(E ∩ F) = `2/36 = 1/18`
P(F) = `18/36 = 1/2`
P(E|F) = `(P(E ∩ F))/(P(F))`
=`1/18 ÷ 1/2`
=`1/9`
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