Two cards are drawn from a well shuffled pack of 52 cards. Find the probability that (1) Both the cards are of

Question 42 of 44

Q. Two cards are drawn from a well shuffled pack of 52 cards. Find the probability that

(1) Both the cards are of different colours.

(2) Both the cards are face cards.

Gujarat GsebGujarat Board (GSEB) HSC Commerce Board 2026Subjective· 3mImportance★★★★★

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Total pairs $=\binom{52}{2}=1326$ . Different colours $=\dfrac{26\times26}{1326}=\dfrac{26}{51}$ ; both face cards $=\dfrac{\binom{12}{2}}{1326}=\dfrac{11}{221}$ .

Two cards are drawn together from $52$ , so the total number of ways is

$\binom{52}{2}=\frac{52\times51}{2}=1326.$

(1) Both cards of different colours: there are $26$ red and $26$ black cards. One card of each colour can be chosen in $26\times26=676$ ways.

$P=\frac{676}{1326}=\frac{26}{51}\approx0.5098.$

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Same / Similar Concept — real previous-year questions on the same or a closely similar concept, not this exact question.

CBSE 2026Set MARCH1 markMCQ
$Q. Which of the following options is true for any event A of the sample space?$
(a) $P(A) < 0$
(b) $0 \le P(A) \ge 1$
(c) $0 \le P(A) \le 1$
(d) $P(A) > 1$
›Reveal solutionSolution

For any event $A$ , $0\le P(A)\le1$ .

By the axiomatic definition of probability, the probability of any event $A$ of the sample space satisfies $0\le P(A)\le1$ . It cannot be negative and cannot exceed $1$ . Option (b) is …

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CBSE 2025Set MARCH1 markMCQ
$Q. What is the probability of having 5 Mondays in the month of February in a year which is not a leap year?$
(a) $0$
(b) $\frac{1}{7}$
(c) $\frac{2}{7}$
(d) $\frac{3}{7}$
›Reveal solutionSolution

A non-leap February has $28$ days $= 4$ full weeks, so every day of the week appears exactly $4$ times; getting $5$ Mondays is impossible, probability $= 0$ — option (a).

GSEB Class-12 Statistics, Probability:

In a non-leap year, February has $28$ days.

$28 = 4 \times 7$

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CBSE 2022Set MARCH1 markMCQ
$Q. What is the other name of the classical definition of probability?$
(a) Mathematical Definition
(b) Axiomatic Definition
(c) Statistical Definition
(d) Geometric Definition
›Reveal solutionSolution

The classical definition of probability is also known as the mathematical (a priori) definition.

Reasoning. The classical approach defines $P(A) = \dfrac{\text{favourable outcomes}}{\text{total equally likely outcomes}}$ purely by reasoning/counting, before any experiment. Hence it is called the mathematical or a prior …

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Q.Two cards are drawn from a well shuffled pack of 52 cards. Find the probability that

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