The probability that at least one of the even | vedclass

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Question

(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(\ov

Vedclass · Accepted Answer

$\frac{6}{5}$

Vedclass · Answer

(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}$.

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

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