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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