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

Question

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 (A)  (1/4)  (B)  (5/4)  (C)  (1/2)  (D)  (3/4)

Tardigrade Admin · Accepted Answer

When a fair die is rolled, then total outcomes =6 Now, P(A ∪ B / C)=(P[(A ∪ B) ∩ C]/P(C)) =(3 / 6/4 / 6) [∵ A ∪ B= 1,2,3,5 and (A ∪ B) ∩ C= 2,3,5 ] =(3/4)

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

$\frac{1}{4}$

$\frac{5}{4}$

$\frac{1}{2}$

$\frac{3}{4}$

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

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∪B/C) is

41​

45​

21​

43​