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Chapter 14: Probability

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This page provides comprehensive Chapter 14: Probability - Standard Worksheet - SJMaths. Standard level practice worksheet for Class 10 Probability. Practice questions on dice, coins, cards, and other probability concepts for CBSE Board Exams.

Standard Level Worksheet

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  1. Question 1: Two dice are thrown simultaneously. Find the probability of getting a doublet (same number on both dice).
    Solution:
    Step 1: Total outcomes when two dice are thrown = $6 \times 6 = 36$.
    Step 2: Favourable outcomes (doublets): $(1,1), (2,2), (3,3), (4,4), (5,5), (6,6)$. Number of favourable outcomes = 6.
    Step 3: Probability $= \frac{6}{36} = \frac{1}{6}$.
    Answer: 1/6.
  2. Question 2: A card is drawn from a well-shuffled pack of 52 cards. Find the probability of getting a king of red colour.
    Solution:
    Step 1: Total cards = 52.
    Step 2: Red kings are King of Hearts and King of Diamonds. Total red kings = 2.
    Step 3: Probability $= \frac{2}{52} = \frac{1}{26}$.
    Answer: 1/26.
  3. Question 3: Find the probability that a leap year selected at random will contain 53 Sundays.
    Solution:
    Step 1: A leap year has 366 days = 52 weeks + 2 days.
    Step 2: The remaining 2 days can be: (Sun, Mon), (Mon, Tue), (Tue, Wed), (Wed, Thu), (Thu, Fri), (Fri, Sat), (Sat, Sun). Total 7 possibilities.
    Step 3: Favourable outcomes (containing Sunday): (Sun, Mon) and (Sat, Sun). Count = 2.
    Step 4: Probability $= \frac{2}{7}$.
    Answer: 2/7.
  4. Question 4: A bag contains 3 red balls and 5 black balls. A ball is drawn at random. What is the probability that the ball drawn is (i) red? (ii) not red?
    Solution:
    Step 1: Total balls $= 3 + 5 = 8$.
    Step 2: (i) P(Red) $= \frac{3}{8}$.
    Step 3: (ii) P(Not Red) $= 1 - P(\text{Red}) = 1 - \frac{3}{8} = \frac{5}{8}$.
    Answer: (i) 3/8, (ii) 5/8.
  5. Question 5: A box contains 90 discs which are numbered from 1 to 90. If one disc is drawn at random from the box, find the probability that it bears (i) a two-digit number (ii) a perfect square number.
    Solution:
    Step 1: Total discs = 90.
    Step 2: (i) Two-digit numbers are 10 to 90. Count $= 90 - 9 = 81$. Probability $= \frac{81}{90} = \frac{9}{10}$.
    Step 3: (ii) Perfect squares: 1, 4, 9, 16, 25, 36, 49, 64, 81. Count = 9. Probability $= \frac{9}{90} = \frac{1}{10}$.
    Answer: (i) 9/10, (ii) 1/10.
  6. Question 6: A lot consists of 144 ball pens of which 20 are defective and the others are good. Nuri will buy a pen if it is good, but will not buy if it is defective. The shopkeeper draws one pen at random and gives it to her. What is the probability that (i) She will buy it? (ii) She will not buy it?
    Solution:
    Step 1: Total pens = 144. Defective = 20. Good $= 144 - 20 = 124$.
    Step 2: (i) P(Buy) = P(Good) $= \frac{124}{144} = \frac{31}{36}$.
    Step 3: (ii) P(Not Buy) = P(Defective) $= \frac{20}{144} = \frac{5}{36}$.
    Answer: (i) 31/36, (ii) 5/36.
  7. Question 7: One card is drawn from a well-shuffled deck of 52 cards. Find the probability of getting (i) a face card (ii) a spade.
    Solution:
    Step 1: Total cards = 52.
    Step 2: (i) Face cards (J, Q, K) in 4 suits $= 3 \times 4 = 12$. Probability $= \frac{12}{52} = \frac{3}{13}$.
    Step 3: (ii) Spade cards = 13. Probability $= \frac{13}{52} = \frac{1}{4}$.
    Answer: (i) 3/13, (ii) 1/4.
  8. Question 8: A game consists of tossing a one rupee coin 3 times and noting its outcome each time. Find the probability of getting at least 2 heads.
    Solution:
    Step 1: Total outcomes = 8 (HHH, HHT, HTH, HTT, THH, THT, TTH, TTT).
    Step 2: At least 2 heads means 2 or 3 heads: {HHH, HHT, HTH, THH}.
    Step 3: Favourable outcomes = 4. Probability $= \frac{4}{8} = \frac{1}{2}$.
    Answer: 1/2.
  9. Question 9: A die is thrown once. Find the probability of getting (i) an even prime number (ii) a number greater than 4.
    Solution:
    Step 1: Total outcomes = {1, 2, 3, 4, 5, 6}.
    Step 2: (i) Even prime number is only 2. Count = 1. Probability $= \frac{1}{6}$.
    Step 3: (ii) Numbers greater than 4 are {5, 6}. Count = 2. Probability $= \frac{2}{6} = \frac{1}{3}$.
    Answer: (i) 1/6, (ii) 1/3.
  10. Question 10: A bag contains lemon flavoured candies only. Malini takes out one candy without looking into the bag. What is the probability that she takes out (i) an orange flavoured candy? (ii) a lemon flavoured candy?
    Solution:
    Step 1: (i) There are no orange candies. It is an impossible event. Probability = 0.
    Step 2: (ii) All candies are lemon. It is a sure event. Probability = 1.
    Answer: (i) 0, (ii) 1.
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