Class 10 Mathematics: Probability important questions

Probability is a chapter of Class 10 Mathematics for the CBSE. These 14 questions are marked Very Important, Important or Practice, and each answer has been checked by our team. Use them to revise, not as a prediction of what will come in the exam.

1. Practice · 1 marks

   1. Two dice are rolled together. The probability that 6 comes up at least once is: (a) 1/6 (b) 7/36 (c) 11/36 (d) 13/36

   (c) 11/36 P(no 6) = 25/36, so P(at least one 6) = 11/36.

2. Important · 3 marks

   2. Two coins are tossed together. Find the probability of getting (i) at least one head, (ii) at most one tail, (iii) a head and a tail.

   Outcomes: HH, HT, TH, TT. (i) At least one head: 3/4. (ii) At most one tail: HH, HT, TH = 3/4. (iii) One head and one tail: HT, TH = 2/4 = 1/2.

3. Practice · 1 marks

   3. A square board of side 2a units circumscribes a red circle. A dot is placed at random on the board. The probability that it lands outside the circle (the shaded corners) is: (a) π/4 (b) (4 − π)/4 (c) (π − 4)/4 (d) 4/π

   (b) (4 − π)/4 The circle has radius a. Shaded area = 4a² − πa², so P = (4a² − πa²)/4a² = (4 − π)/4.

4. Practice · 1 marks

   4. 2 cards of hearts and 4 cards of spades are missing from a pack of 52 cards. A card is drawn at random from the rest. The probability of getting a black card is: (a) 22/52 (b) 22/46 (c) 24/52 (d) 24/46

   (b) 22/46 46 cards remain, of which 26 − 4 = 22 are black.

5. Practice · 1 marks

   5. A bag contains 24 balls: 4 blue, 11 green and the rest white. One ball is drawn at random. The probability that it is white is: (A) 1/6 (B) 3/8 (C) 11/24 (D) 5/8

   (B) 3/8 White balls = 24 − 15 = 9, so P = 9/24 = 3/8.

6. Practice · 1 marks

   6. A card is drawn from a well-shuffled deck of 52 playing cards. The probability of getting a red face card is: (A) 3/13 (B) 1/2 (C) 3/52 (D) 3/26

   (D) 3/26 There are 6 red face cards, so P = 6/52 = 3/26.

7. Important · 2 marks

   7. Two dice, each with faces numbered 4, 6, 7, 9, 11, 12, are rolled together. Find the probability that the product of the numbers obtained is odd.

   Total outcomes = 6 × 6 = 36. The product is odd only if both numbers are odd (7, 9 or 11): 3 × 3 = 9 outcomes. P = 9/36 = 1/4.

8. Important · 2 marks

   8. How many three-digit positive integers have hundreds digit 8 and units digit 5? Find the probability of selecting one such number from all three-digit numbers.

   The numbers are 805, 815, …, 895: 10 numbers. There are 900 three-digit numbers, so P = 10/900 = 1/90.

9. Practice · 1 marks

   9. A pair of dice is tossed. The probability of not getting a sum of 8 is: (A) 5/36 (B) 31/36 (C) 5/18 (D) 5/9

   (B) 31/36 Sum 8: (2,6), (3,5), (4,4), (5,3), (6,2) = 5 of 36. P(not 8) = 1 − 5/36 = 31/36.

10. Important · 3 marks

    10. Vidhi and Unnati each flip a coin three times to decide who drives. Vidhi drives if she gets two heads in a row; Unnati drives if she gets a head immediately followed by a tail. Who is more likely to drive? Justify.

    Each has 8 equally likely outcomes. Vidhi (HH in a row): HHH, HHT, THH = 3, so P = 3/8. Unnati (H followed by T): HHT, HTH, HTT, THT = 4, so P = 4/8 = 1/2. Unnati has the greater probability of driving.

11. Practice · 1 marks

    11. T-shirts numbered 4 to 99 are in a box. Gunika takes one at random. The probability that its number is a perfect square or a perfect cube is: (A) 1/12 (B) 1/32 (C) 11/96 (D) 5/48

    (D) 5/48 There are 96 T-shirts. Perfect squares: 4, 9, 16, 25, 36, 49, 64, 81; perfect cubes: 8, 27, 64 (64 is counted once). That is 10 numbers, so P = 10/96 = 5/48.

12. Practice · 1 marks

    12. Two dice are rolled together. The probability of getting a number less than 4 on each die is: (A) 1/4 (B) 1/9 (C) 1/36 (D) 1/6

    (A) 1/4 Favourable outcomes: (1,1), (1,2), (1,3), (2,1), (2,2), (2,3), (3,1), (3,2), (3,3) = 9 of 36, so P = 9/36 = 1/4.

13. Practice · 1 marks

    13. 2 diamonds and 4 spades are missing from a pack of 52 cards. One card is drawn at random. The probability of getting a heart is: (A) 13/52 (B) 13/46 (C) 11/52 (D) 11/46

    (B) 13/46 52 − 6 = 46 cards remain, and all 13 hearts are there, so P = 13/46.

14. Important · 2 marks

    14. Two dice are thrown together. Find the probability that the product of the numbers on them is a prime number.

    Total outcomes = 36. A product is prime only when one die shows 1 and the other a prime: (1,2), (1,3), (1,5), (2,1), (3,1), (5,1) = 6 outcomes. P = 6/36 = 1/6.