Question 1

A die is thrown once. The probability of getting a prime number is:

Accepted Answer

**Answer: (a)** $\dfrac{1}{2}$ Prime numbers on a die are $2,3,5$ (three outcomes). $P=\dfrac{3}{6}=\dfrac{1}{2}.$

Question 2

Which of the following cannot be the probability of an event?

Accepted Answer

**Answer: (a)** $-1.5$ The probability of any event always satisfies $0\le P(E)\le 1$, so a negative value like $-1.5$ is impossible.

Question 3

One card is drawn at random from a well-shuffled deck of $52$ cards. The probability of getting a red king is:

Accepted Answer

**Answer: (a)** $\dfrac{1}{26}$ There are $2$ red kings (king of hearts and king of diamonds). $P=\dfrac{2}{52}=\dfrac{1}{26}.$

Question 4

Two dice are thrown together. The probability that the sum of the numbers appearing on them is a perfect square is:

Accepted Answer

**Answer: (a)** $\dfrac{7}{36}$ Possible sums range from $2$ to $12$; the perfect squares are $4$ and $9$. Sum $=4$: $(1,3),(2,2),(3,1)=3$ ways. Sum $=9$: $(3,6),(4,5),(5,4),(6,3)=4$ ways. Total $=7.$ $P=\dfrac{7}{36}.$

Question 5

**Assertion (A):** When a die is thrown once, the probability of getting a number greater than $4$ is $\dfrac{1}{3}.$ **Reason (R):** The probability of an event $=\dfrac{	ext{number of favourable outcomes}}{	ext{total number of outcomes}}.$

Accepted Answer

**Answer: (a)** Both A and R are true and R is the correct explanation of A. Numbers greater than $4$ are $5$ and $6$, so $P=\dfrac{2}{6}=\dfrac{1}{3}$, obtained exactly by the formula in R.

Question 6

A bag contains $5$ red, $8$ white and $7$ black balls. A ball is drawn at random. Find the probability that it is (i) red, (ii) not black.

Accepted Answer

Total balls $=5+8+7=20.$ **(i)** $P(	ext{red})=\dfrac{5}{20}=\dfrac{1}{4}.$ **(ii)** Black balls $=7$, so $P(	ext{not black})=1-\dfrac{7}{20}=\dfrac{13}{20}.$

Question 7

Cards numbered $1$ to $25$ are placed in a box and mixed thoroughly. One card is drawn at random. Find the probability that the number on the drawn card is divisible by $3$ or $5$.

Accepted Answer

Divisible by $3$: $3,6,9,12,15,18,21,24\Rightarrow 8$ numbers. Divisible by $5$: $5,10,15,20,25\Rightarrow 5$ numbers. Divisible by both ($15$): $1$ number. Favourable $=8+5-1=12.$ $P=\dfrac{12}{25}.$

Question 8

Two dice are thrown simultaneously. Find the probability that (i) the sum of the numbers is $7$, (ii) the sum is a prime number, (iii) the same number appears on both dice.

Accepted Answer

Total outcomes $=36.$ **(i)** Sum $=7$: $(1,6),(2,5),(3,4),(4,3),(5,2),(6,1)=6$ ways. $P=\dfrac{6}{36}=\dfrac{1}{6}.$ **(ii)** Prime sums are $2,3,5,7,11$ with $1+2+4+6+2=15$ ways. $P=\dfrac{15}{36}=\dfrac{5}{12}.$ **(iii)** Doublets: $(1,1),(2,2),(3,3),(4,4),(5,5),(6,6)=6$ ways. $P=\dfrac{6}{36}=\dfrac{1}{6}.$

Question 9

From a well-shuffled deck of $52$ cards, all the three face cards of spades (king, queen and jack of spades) are removed. One card is then drawn at random from the remaining cards. Find the probability that the drawn card is (i) a heart, (ii) a queen, (iii) a black card.

Accepted Answer

Remaining cards $=52-3=49.$ **(i)** Hearts are untouched $=13.$ $P(	ext{heart})=\dfrac{13}{49}.$ **(ii)** Only the queen of spades was removed, so $3$ queens remain. $P(	ext{queen})=\dfrac{3}{49}.$ **(iii)** Black cards were $26$; removing $3$ spades leaves $23.$ $P(	ext{black})=\dfrac{23}{49}.$

Question 10

A number $x$ is selected at random from the numbers $1, 2, 3, 4$ and a number $y$ is selected at random from the numbers $1, 4, 9, 16$. Find the probability that the product $xy$ is less than $16$.

Accepted Answer

Total outcomes $=4	imes 4=16.$ Count the pairs with $xy<16$: $x=1$: $y=1,4,9$ give $1,4,9$ (all $<16$) $\Rightarrow 3.$ $x=2$: $y=1,4$ give $2,8$ $\Rightarrow 2.$ $x=3$: $y=1,4$ give $3,12$ $\Rightarrow 2.$ $x=4$: $y=1$ gives $4$ $\Rightarrow 1.$ Favourable $=3+2+2+1=8.$ $P(xy<16)=\dfrac{8}{16}=\dfrac{1}{2}.$

Question 11

Two dice are thrown together. Find the probability that (i) the product of the numbers is $12$, (ii) the sum of the numbers is $8$, (iii) a doublet appears, (iv) the sum is divisible by $3$, (v) both numbers are odd.

Accepted Answer

Total outcomes $=36.$ **(i)** Product $12$: $(2,6),(6,2),(3,4),(4,3)=4$ ways. $P=\dfrac{4}{36}=\dfrac{1}{9}.$ **(ii)** Sum $8$: $(2,6),(6,2),(3,5),(5,3),(4,4)=5$ ways. $P=\dfrac{5}{36}.$ **(iii)** Doublets $=6$ ways. $P=\dfrac{6}{36}=\dfrac{1}{6}.$ **(iv)** Sum divisible by $3$ (sums $3,6,9,12$): $2+5+4+1=12$ ways. $P=\dfrac{12}{36}=\dfrac{1}{3}.$ **(v)** Both odd ($1,3,5$ on each): $3	imes 3=9$ ways. $P=\dfrac{9}{36}=\dfrac{1}{4}.$

Question 12

A box contains $12$ balls, out of which $x$ are black. (i) If one ball is drawn at random, write the probability that it is black. (ii) If $6$ more black balls are put in the box, the probability of drawing a black ball is now double what it was in (i). Find $x$. (iii) Using this value of $x$, find the probability of drawing a black ball after the $6$ balls are added.

Accepted Answer

**(i)** $P(	ext{black})=\dfrac{x}{12}.$ **(ii)** After adding $6$ black balls, total $=18$ and black $=x+6$, so $P=\dfrac{x+6}{18}.$ Given this is double the earlier value: $\dfrac{x+6}{18}=2	imes\dfrac{x}{12}=\dfrac{x}{6}.$ Cross-multiplying: $6(x+6)=18x\Rightarrow 6x+36=18x\Rightarrow 12x=36\Rightarrow x=3.$ **(iii)** New probability $=\dfrac{x+6}{18}=\dfrac{9}{18}=\dfrac{1}{2}.$

Question 13

At a school fair, a game uses a fair spinning wheel divided into $8$ equal sectors numbered $1, 2, 3, \ldots, 8$ . A player wins a prize depending on where the pointer stops. Assume each number is equally likely.

(i) Find the probability that the pointer stops at an odd number.

(ii) Find the probability that it stops at a number that is a multiple of $3$ .

(iii) Find the probability that it stops at a prime number.

Accepted Answer

Total outcomes $=8.$ **(i)** Odd numbers: $1,3,5,7\Rightarrow 4.$ $P(	ext{odd})=\dfrac{4}{8}=\dfrac{1}{2}.$ **(ii)** Multiples of $3$: $3,6\Rightarrow 2.$ $P=\dfrac{2}{8}=\dfrac{1}{4}.$ **(iii)** Primes: $2,3,5,7\Rightarrow 4.$ $P(	ext{prime})=\dfrac{4}{8}=\dfrac{1}{2}.$

Question 14

Are these Probability important questions free?

Accepted Answer

Yes. All 13 CBSE Class 10 Maths important questions for Probability are free, with full model answers and no login required.

Question 15

Do these Probability questions follow the latest CBSE syllabus?

Accepted Answer

Yes — they are aligned to the NCERT 2026–27 syllabus for CBSE Class 10 Maths, so nothing here is outside the current course.

Question 16

How should I practise the Probability important questions?

Accepted Answer

Attempt each question on paper first, then reveal the model answer to check your method — not just the final result. Re-do anything you got wrong the same day.

Question 17

What types of questions are covered for Probability?

Accepted Answer

A full mix — multiple-choice questions, assertion–reason questions, very short answer questions, short answer questions, long answer questions, case-based questions — so every format in the CBSE paper is covered.

Question type	Count	Marks
MCQ	4	1
Assertion–Reason	1	1
Very Short	2	2
Short Answer	3	3
Long Answer	2	5
Case-based	1	4

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