Class 10 Mathematics: Probability important questions

Probability is a chapter of Class 10 Mathematics for the Andhra Pradesh State Board. These 17 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. Important · 4 marks

   1. A die is thrown once. Find the probability of getting i) 8 ii) a number less than 6 iii) a prime number iv) a composite number.

   i) 8 is impossible: P = 0. ii) 1 to 5: P = 5/6. iii) Primes 2, 3, 5: P = 3/6 = 1/2. iv) Composites 4, 6: P = 2/6 = 1/3.

2. Very Important · 8 marks

   2. One card is drawn from a well-shuffled deck of 52 cards. Find the probability of getting i) a black queen ii) a face card iii) the jack of diamonds iv) a club.

   i) 2 black queens: 2/52 = 1/26. ii) 12 face cards: 12/52 = 3/13. iii) 1 jack of diamonds: 1/52. iv) 13 clubs: 13/52 = 1/4.

3. Practice · 1 marks

   3. If P(E) = 0.05, what is the probability of 'not E'?

   P(not E) = 1 − P(E) = 1 − 0.05 = 0.95.

4. Important · 4 marks

   4. One card is drawn from a well-shuffled deck of 52 cards. Find the probability of getting i) a black king ii) a red face card.

   i) There are 2 black kings (spades and clubs): P = 2/52 = 1/26. ii) Red face cards: J, Q, K of hearts and diamonds = 6: P = 6/52 = 3/26.

5. Very Important · 8 marks

   5. A box contains 100 discs numbered 1 to 100. One disc is drawn at random. Find the probability that it bears i) a two-digit number ii) a perfect square iii) a number divisible by 5 iv) a number divisible by 10.

   i) Two-digit numbers 10 to 99: 90, so P = 90/100 = 9/10. ii) Perfect squares 1, 4, 9, …, 100: 10, so P = 10/100 = 1/10. iii) Multiples of 5 up to 100: 20, so P = 20/100 = 1/5. iv) Multiples of 10 up to 100: 10, so P = 10/100 = 1/10.

6. Practice · 1 marks

   6. P(E) + P(not E) = ? A) 0 B) 1 C) −1 D) More than 1

   B) 1. An event and its complement together cover every outcome.

7. Important · 4 marks

   7. One card is drawn from a well-shuffled deck of 52 cards. Find the probability that it is an ace. Then create four similar questions.

   P(ace) = 4/52 = 1/13. Four more questions with answers: 1) P(red card) = 26/52 = 1/2. 2) P(king of hearts) = 1/52. 3) P(face card: J, Q or K) = 12/52 = 3/13. 4) P(spade) = 13/52 = 1/4.

8. Very Important · 8 marks

   8. A spinner's arrow comes to rest at one of the numbers 1, 2, 3, 4, 5, 6, 7, 8, all equally likely. Find the probability that it points at i) 8 ii) an odd number iii) a number greater than 3 iv) a number less than 9

   i) 1/8 ii) 1, 3, 5, 7: 4/8 = 1/2 iii) 4, 5, 6, 7, 8: 5/8 iv) all 8 numbers: 8/8 = 1

9. Practice · 1 marks

   9. When a fair coin is tossed once, the probability of getting a head is A) 1 B) 1/2 C) 2 D) 0

   B) 1/2. There are two equally likely outcomes, head and tail.

10. Important · 4 marks

    10. A die is thrown once. What is the probability of getting a number greater than 4? Now create four such questions.

    Numbers greater than 4: 5 and 6, so P = 2/6 = 1/3. Four more questions with answers: 1) P(even number) = 3/6 = 1/2. 2) P(prime number: 2, 3, 5) = 3/6 = 1/2. 3) P(number less than 3) = 2/6 = 1/3. 4) P(getting 6) = 1/6.

11. Very Important · 8 marks

    11. A piggy bank contains a hundred 50p coins, fifty ₹1 coins, twenty ₹2 coins and ten ₹5 coins. If each coin is equally likely to fall out when the bank is turned upside down, find the probability that the coin i) will be a 50p coin ii) will not be a ₹5 coin iii) will be a ₹2 coin iv) will not be a ₹1 coin.

    Total coins = 100 + 50 + 20 + 10 = 180. i) P(50p) = 100/180 = 5/9. ii) P(not ₹5) = 170/180 = 17/18. iii) P(₹2) = 20/180 = 1/9. iv) P(not ₹1) = 130/180 = 13/18.

12. Practice · 1 marks

    12. A die is thrown once to find the probability P(E) of getting an even number. Which statement is true? A) Getting even and odd numbers are equally likely, therefore P(E) = 0.5 B) P(E) = n(E)/n(S) = 3/6 C) Both A and B D) Neither A nor B

    C) Both A and B There are 3 even outcomes (2, 4, 6) out of 6, so P(E) = 3/6 = 0.5. Both statements give the same correct value.

13. Important · 4 marks

    13. Create any four different probability questions involving two dice thrown simultaneously, similar to this example: What is the probability of getting even numbers on the top faces of both dice when two dice are thrown simultaneously?

    Two dice give 36 equally likely outcomes. Sample questions with answers: 1) Probability that the sum is 7: (1,6),(2,5),(3,4),(4,3),(5,2),(6,1) = 6/36 = 1/6. 2) Probability of a doublet (same number on both): 6/36 = 1/6. 3) Probability that the sum is more than 10: (5,6),(6,5),(6,6) = 3/36 = 1/12. 4) Probability that the product is 6: (1,6),(2,3),(3,2),(6,1) = 4/36 = 1/9.

14. Very Important · 8 marks

    14. One card is drawn from a well-shuffled deck of 52 cards. Find the probability that the card is i) a numbered card ii) a letter card (A, J, Q, K) iii) not a face card iv) a diamond but not a face card.

    i) Numbered cards 2 to 10 in each suit: 9 × 4 = 36, so P = 36/52 = 9/13. ii) Letter cards A, J, Q, K: 4 × 4 = 16, so P = 16/52 = 4/13. iii) Face cards (J, Q, K) = 12, so not a face card = 40, and P = 40/52 = 10/13. iv) Diamonds = 13, of which 3 are face cards, so 10 cards; P = 10/52 = 5/26.

15. Practice · 1 marks

    15. A friend says the probability of an event can be 5/3. How would you respond? A) Agree, because probability can be any positive value B) Politely explain that the probability of an event always lies between 0 and 1 (0 ≤ P(E) ≤ 1), so it cannot be 5/3 C) Ignore the friend's opinion D) Say the answer is wrong without giving any reason

    B) Probability always lies between 0 and 1. Since 5/3 > 1, it cannot be a probability.

16. Important · 4 marks

    16. A child's die has the letters A, B, C, D, E, A on its six faces. The die is thrown once. Using this, create four probability questions (for example: what is the probability of getting D?).

    Six equally likely outcomes, with A appearing twice. 1) P(getting A) = 2/6 = 1/3. 2) P(getting D) = 1/6. 3) P(getting a vowel, A or E) = 3/6 = 1/2. 4) P(not getting A) = 4/6 = 2/3. (Also: P(getting F) = 0, an impossible event.)

17. Very Important · 8 marks

    17. A spinner's arrow comes to rest at one of the numbers 1 to 8, all equally likely. Find the probability that it points at i) 8 ii) an odd number iii) a number greater than 3 iv) a number less than or equal to 8

    There are 8 outcomes. i) P(8) = 1/8. ii) Odd numbers 1, 3, 5, 7: P = 4/8 = 1/2. iii) Greater than 3: 4, 5, 6, 7, 8, so P = 5/8. iv) Every number is ≤ 8, so P = 8/8 = 1 (a sure event).