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  4. A fair die is rolled. Consider the events A= 1,3,5 B= 2,3 and C= 2,3,4,5 . Then, the conditional probability P(A ∪ B / C) is

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Q. A fair die is rolled. Consider the events $A=\{1,3,5\}, B=\{2,3\}$ and $C=\{2,3,4,5\}$. Then, the conditional probability $P(A \cup B / C)$ is

AMUAMU 2015Probability - Part 2

Solution:

When a fair die is rolled, then total outcomes $=6$
Now, $P(A \cup B / C)=\frac{P[(A \cup B) \cap C]}{P(C)}$
$=\frac{3 / 6}{4 / 6}$
$[\because A \cup B=\{1,2,3,5\}$ and $(A \cup B) \cap C=\{2,3,5\}]$
$=\frac{3}{4}$