If $A$ and $B$ are two mutually exclusive events, then $P\,(A + B) = $
$P\,(A) + P\,(B) - P\,(AB)$
$P\,(A) - P\,(B)$
$P\,(A) + P\,(B)$
$P\,(A) + P\,(B) + P\,(AB)$
(c) $P(A) + P(B)$ (Fundamental concept).
In an entrance test that is graded on the basis of two examinations, the probability of a randomly chosen student passing the first examination is $0.8$ and the probability of passing the second examination is $0.7 .$ The probability of passing at least one of them is $0.95 .$ What is the probability of passing both ?
If ${A_1},\,{A_2},…{A_n}$ are any $n$ events, then
Two cards are drawn at random and without replacement from a pack of $52$ playing cards. Finds the probability that both the cards are black.
An electronic assembly consists of two subsystems, say, $A$ and $B$. From previous testing procedures, the following probabilities are assumed to be known :
$\mathrm{P}$ $( A$ fails $)=0.2$
$P(B$ fails alone $)=0.15$
$P(A$ and $ B $ fail $)=0.15$
Evaluate the following probabilities $\mathrm{P}(\mathrm{A}$ fails alone $)$
Three persons $P, Q$ and $R$ independently try to hit a target . If the probabilities of their hitting the target are $\frac{3}{4},\frac{1}{2}$ and $\frac{5}{8}$ respectively, then the probability that the target is hit by $P$ or $Q$ but not by $R$ is
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