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 chances to fail in Physics are $20\%$ and the chances to fail in Mathematics are $10\%$. What are the chances to fail in at least one subject ………… $\%$
The probability that a student will pass the final examination in both English and Hindi is $0.5$ and the probability of passing neither is $0.1$. If the probability of passing the English examination is $0.75$, what is the probability of passing the Hindi examination?
Three coins are tossed simultaneously. Consider the event $E$ ' three heads or three tails', $\mathrm{F}$ 'at least two heads' and $\mathrm{G}$ ' at most two heads '. Of the pairs $(E,F)$, $(E,G)$ and $(F,G)$, which are independent? which are dependent ?
A bag contains $9$ discs of which $4$ are red, $3$ are blue and $2$ are yellow. The discs are similar in shape and size. A disc is drawn at random from the bag. Calculate the probability that it will be either red or blue.
Two students Anil and Ashima appeared in an examination. The probability that Anil will qualify the examination is $0.05$ and that Ashima will qualify the examination is $0.10 .$ The probability that both will qualify the examination is $0.02 .$ Find the probability that Both Anil and Ashima will not qualify the examination.
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