If two balanced coins are tossed, then find the probability of (1) getting one head and one tail (2) getting a

Question 23 of 44

Q. If two balanced coins are tossed, then find the probability of

(1) getting one head and one tail

(2) getting at least one head.

Gujarat GsebGujarat Board (GSEB) HSC Commerce Board 2022Subjective· 3mImportance★★★★★

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Sample space $=\{HH,HT,TH,TT\}$ , $n(S)=4$ . (1) $\{HT,TH\}\Rightarrow \tfrac12$ ; (2) $\{HH,HT,TH\}\Rightarrow \tfrac34$ .

Sample space (two balanced coins):

$S=\{HH,\ HT,\ TH,\ TT\},\qquad n(S)=4.$

(1) One head and one tail. Favourable: $\{HT, TH\}$ , so $n=2$ .

$P=\frac{2}{4}=\frac{1}{2}.$

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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.If two balanced coins are tossed, then find the probability of

Concept understanding — Approaches to Probability — Classical, Relative Frequency and Axiomatic

Q.If two balanced coins are tossed, then find the probability of

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