Question:
The probability of having a king and a queen when the two cards are drawn at random from a pack of 52 cards is:
The probability of having a king and a queen when the two cards are drawn at random from a pack of 52 cards is:
Updated On: Jul 7, 2022
- $\frac{16}{663}$
- $\frac{8}{663}$
- $\frac{4}{663}$
- $\frac{2}{663}$
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The Correct Option is B
Solution and Explanation
Number of ways of getting king alone = ${^4C_1}$
Number of ways of getting queen alone = ${^4C_1}$
Total number of ways in which 2 cards are drawn from a pack of 52 cards = ${^{52}C_2}$.
$\Rightarrow $ Required probability
$ = \frac{^{4}C_{1} \times^{4}C_{1}}{^{52}C_{2} } = \frac{4 \times4 \times2}{52\times51} = \frac{8}{663} $
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Notes on Multiplication Theorem on Probability
Concepts Used:
Multiplication Theorem on Probability
In accordance with the multiplication rule of probability, the probability of happening of both the events A and B is equal to the product of the probability of B occurring and the conditional probability that event A happens given that event B occurs.
Let's assume, If A and B are dependent events, then the probability of both events occurring at the same time is given by:
\(P(A\cap B) = P(B).P(A|B)\)
Let's assume, If A and B are two independent events in an experiment, then the probability of both events occurring at the same time is given by:
\(P(A \cap B) = P(A).P(B)\)
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