If $A$ and $B$ are two independent events, then $P\,(A + B) = $
$P\,(A) + P\,(B) - P\,(A)\,P\,(B)$
$P\,(A) - P\,(B)$
$P\,(A) + P\,(B)$
$P\,(A) + P\,(B) + P\,(A)\,P\,(B)$
(a) It is obvious.
The probability that $A$ speaks truth is $\frac{4}{5}$, while this probability for $B$ is $\frac{3}{4}$. The probability that they contradict each other when asked to speak on a fact
If $A$ and $B$ are any two events, then $P(A \cup B) = $
Given that the events $A$ and $B$ are such that $P(A)=\frac{1}{2}, P(A \cup B)=\frac{3}{5}$ and $\mathrm{P}(\mathrm{B})=p .$ Find $p$ if they are mutually exclusive.
In a class of $125$ students $70$ passed in Mathematics, $55$ in Statistics and $30$ in both. The probability that a student selected at random from the class has passed in only one subject is
Probability that a student will succeed in $IIT$ entrance test is $0.2$ and that he will succeed in Roorkee entrance test is $0.5$. If the probability that he will be successful at both the places is $0.3$, then the probability that he does not succeed at both the places is
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