Probability that at least one of A and B occurs is 0.6 . If A and B occur simultaneously with probab

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14.Probability

medium

The probability that at least one of $A$ and $B$ occurs is $0.6$. If $A$ and $B$ occur simultaneously with probability $0.3$, then $P(A') + P(B') = $

A

$0.9$

B

$1.15$

C

$1.1$

D

$1.2$

Solution

(c) $1 – P(A' \cap B') = 0.6,$ $P(A \cap B) = 0.3,$ then

$P(A' \cup B') = P(A') + P(B') – P(A' \cap B')$

$⇒$ $1 – P(A \cap B) = P(A') + P(B') – 0.4$

$⇒$ $P(A') + P(B') = 0.7 + 0.4 = 1.1$.

Standard 11

Mathematics

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