Probability that at least one of events A and B occurs is 3/5 . If A and B occur simultaneously with

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14.Probability

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The probability that at least one of the events $A$ and $B$ occurs is $3/5$. If $A$ and $B$ occur simultaneously with probability $1/5$, then $P(A') + P(B')$ is

A

$\frac{2}{5}$

B

$\frac{4}{5}$

C

$\frac{6}{5}$

D

$\frac{7}{5}$

Solution

(c) Given $P(A \cup B) = \frac{3}{5}$ and $P(A \cap B) = \frac{1}{5}$

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

$\frac{3}{5} = 1 – P(\overline A ) + 1 – P(\overline B ) – \frac{1}{5}$

$2 – \frac{4}{5} = P(\overline A ) + P(\overline B )$$ \Rightarrow $$P(\overline A ) + P(\overline B ) = \frac{6}{5}$.

Standard 11

Mathematics

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