Question:medium
A die is rolled. Consider the following events:
$A = \{1, 2, 5\}$, $B = \{3, 5\}$, $C = \{2, 3, 4, 5\}$
Find the following conditional probabilities:
(i) $P(A|C)$ and $P(C|A)$
(ii) $P(A \cap B|C)$ and $P(A \cup B|C)$}
A die is rolled. Consider the following events:
$A = \{1, 2, 5\}$, $B = \{3, 5\}$, $C = \{2, 3, 4, 5\}$
Find the following conditional probabilities:
(i) $P(A|C)$ and $P(C|A)$
(ii) $P(A \cap B|C)$ and $P(A \cup B|C)$}
$A = \{1, 2, 5\}$, $B = \{3, 5\}$, $C = \{2, 3, 4, 5\}$
Find the following conditional probabilities:
(i) $P(A|C)$ and $P(C|A)$
(ii) $P(A \cap B|C)$ and $P(A \cup B|C)$}
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For discrete sample spaces, you can find conditional probability $P(X|Y)$ quickly by ignoring the main sample space $S$ entirely. Treat set $Y$ as your new universe, and count how many elements of $X$ live inside it!
Updated On: Jul 6, 2026
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