Maharashtra SSC Algebra HOTS Questions with Answers – Probability | Class 10 Board Exam 2027

Asked in: March 2025 board paper; July 2024 board paper (options \(\dfrac{2}{3}\), 1.5, 15%, 0.7, answer 1.5); July 2025 board paper (options 0.6, 2.0, 0.15, 0.75, answer 2.0)

Q.1 Which number cannot represent a probability?

Asked in: March 2025, March 2026 and June 2026 board papers (June 2026 also asked n(S)); March 2024 (2-mark activity on the same sample space)

Q.2 Two coins are tossed simultaneously. Write the sample space S.

Asked in: June 2026 board paper; July 2024 (1 mark: sample space of one die); March 2026 (2-mark activity: prime number on one die, answer 1/2)

Q.3 If one die is rolled, then write the sample space (S), \(n(S)\), event A in the set form and \(n(A)\).
Event A: getting odd number on the upper face.

Asked in: March 2026 board paper; March 2024 board paper (activity: write events “at least one head” and “no head”)

Q.4 If two coins are tossed simultaneously, find the probability of the event, “getting at least one head.”

Asked in: March 2025 board paper; March 2024 board paper (1 mark: write this sample space)

Q.5 A two digit number is to be formed from the digits 2, 3, 5 without repetition of the digits. Complete the following activity to find the probability that the number so formed is an odd number.

Activity:
Let S be the sample space.
S = {23, 25, 32, ____, 52, 53}
n(S) = ____
Event A: The number so formed is an odd number.
A = {23, 25, ____, 53}
n(A) = 4
P(A) = ____ / n(S) ............ (Formula)
P(A) = ____ / 6
P(A) = ____ / 3.

Asked in: June 2026 board paper

Q.6 A two digit number is formed using digits 2, 3, 5, 7, 9 without repetition. What is the probability that the number formed is:
(a) an odd number.
(b) a multiple of 5.

Asked in: July 2025 board paper; March 2024 board paper (2 marks: probability of a face card)

Q.7 A card is drawn from a well shuffled pack of 52 playing cards. Complete the following activity to find the probability of the following events:
(a) A red card (b) A face card.

Activity:
Let ‘S’ is the sample space \(\therefore\) n(S) = ____
Event A: Card drawn is a red card. Total red cards = ____ \(\therefore\) n(A) = ____
\(\therefore P(A) = \dfrac{n(A)}{n(S)}\) ...... Formula
\(\therefore P(A) = \dfrac{26}{52}\) \(\therefore\) P(A) = ____
Event B: Card drawn is a face card. Total face cards = 12 \(\therefore\) n(B) = ____
\(\therefore P(B) = \dfrac{n(B)}{n(S)}\) ...... Formula
\(\therefore P(B) = \dfrac{12}{52}\) \(\therefore\) P(B) = ____

Asked in: July 2024 board paper

Q.8 The numbers 2, 4, 6, 8, 10, 12 are on the surface of one die. If this die is rolled once, then complete the activity to find probability of getting a number on upper face is a perfect square.

Activity:
S = {____} \(\therefore\) n(S) = ____
Condition for event B: getting a perfect square on the upper surface of that die.
\(\therefore\) B = {____} \(\therefore\) n(B) = ____
\(P(B) = \dfrac{n(B)}{n(S)} = \dfrac{\text{____}}{6}\) = ____

Asked in: March 2024 board paper

Q.9 One coin and a die are thrown simultaneously. Find the probability of the following events:
Event A: To get a head and a prime number.
Event B: To get a tail and an odd number.

Asked in: March 2026 board paper

Q.10 There are six cards in a box, each bearing a number from 0 to 5. Find the probability of each of the following events, that:
(1) The number on the card drawn is a natural number.
(2) The number on the card drawn is a whole number.

Asked in: March 2025 board paper

Q.11 A committee of two members is to be formed from three boys and two girls. Find the probability of the following events:
Event A: At least one girl must be a member of the committee.
Event B: Committee must be of one boy and one girl.

Asked in: July 2025 board paper; July 2024 board paper (3 marks: two dice, sum a multiple of 5, and sum 25 which is an impossible event, P = 0)

Q.12 Two dice are thrown. Find the probability of the following events:
(a) Event A: The sum of the numbers on their upper faces is at least 9.
(b) Event B: The sum of the numbers on their upper faces is divisible by 5.
(c) Event C: The number on the upper face of the first die is greater than the number on the upper face of the second die.

Q.13 The probability of an impossible event is _____.

Q.14 If \(P(A) = 0.35\), then \(P(A')\) is _____.

Q.15 When three coins are tossed simultaneously, the number of sample points n(S) is _____.

Q.16 If \(n(S) = 40\) and \(P(A) = \dfrac{3}{8}\), find \(n(A)\).

Q.17 A die is rolled. Write the event “getting a multiple of 3” in set form.

Q.18 Three coins are tossed simultaneously. Find the probability of getting exactly two heads.

Q.19 One letter is chosen at random from the letters of the word “EXAMINATION”. Find the probability that the letter chosen is a vowel.

Q.20 (Thinking question) What is the probability that a leap year, selected at random, contains 53 Sundays?

Q.21 A two digit number is formed from the digits 0, 1, 2, 3 without repetition. Find the probability that the number is (a) even (b) prime.

Q.22 A card is drawn from a well shuffled pack of 52 playing cards. Find the probability that the card is (a) a king or a heart (b) neither red nor a king.

Q.23 Two numbers are selected together from 1, 2, 3, 4, 5. Find the probability that (a) their sum is even (b) their product is odd.

Q.24 Two dice are rolled. Find the probability of the following events:
(a) Event A: the product of the numbers on the upper faces is 12.
(b) Event B: both dice show the same number.
(c) Event C: the sum of the numbers is a prime number.

Q.25 Thirty cards numbered 1 to 30 are put in a box and one card is drawn at random. Find the probability that the number on the card is:
(a) a multiple of 3 or 5
(b) a perfect square
(c) a prime number.

Q.26 A bag contains 5 red, 3 white and 2 blue balls of the same size. One ball is drawn at random. Find the probability that the ball drawn is (a) not red (b) white or blue.