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.
There are $26$ black cards in a deck of $52$ cards.
Let $P(A)$ be the probability of getting a black card in the first draw.
$\therefore $ $P(A)=\frac{26}{52}=\frac{1}{2}$
Let $\mathrm{P}(\mathrm{B})$ be the probability of getting a black card on second draw. since the card is not replaced,
$\therefore $ $P(B)=\frac{25}{51}$
Thus, probability of getting both the cards black $=\frac{1}{2} \times \frac{25}{51}=\frac{25}{102}$
An experiment has $10$ equally likely outcomes. Let $\mathrm{A}$ and $\mathrm{B}$ be two non-empty events of the experiment. If $\mathrm{A}$ consists of $4$ outcomes, the number of outcomes that $B$ must have so that $A$ and $B$ are independent, is
If $P\,(A) = \frac{1}{4},\,\,P\,(B) = \frac{5}{8}$ and $P\,(A \cup B) = \frac{3}{4},$ then $P\,(A \cap B) = $
If $A, B, C$ are three events associated with a random experiment, prove that
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Let $A$ and $B$ are two independent events. The probability that both $A$ and $B$ occur together is $1/6$ and the probability that neither of them occurs is $1/3$. The probability of occurrence of $A$ is
An integer is chosen at random from the integers $\{1,2,3, \ldots \ldots . .50\}$. The probability that the chosen integer is a multiple of atleast one of $4,6$ and $7$ is