Probability (Class 10 Mathematics)
Probability is the mathematical study of uncertainty and randomness, with applications in statistics, finance, and science. Understanding basic probability
TL;DR: Probability is the mathematical study of uncertainty and randomness, with applications in statistics, finance, and science. Understanding basic probab…
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Probability is the mathematical study of uncertainty and randomness, with applications in statistics, finance, and science. Understanding basic probability
Probability MCQs with Answers & Explanations
Q1. The probability of an impossible event is:
- Between 0 and 1
- 0.5
- 1
- 0 ✓ (correct)
Explanation: The probability of an impossible event is 0, as it can never occur.
Q2. If a coin is tossed twice, the probability of getting two tails is:
- 1/4 ✓ (correct)
- 1/2
- 3/4
- 1
Explanation: Probability = (Favorable outcomes) / (Total outcomes) = 1/4 for getting two tails (TT out of HH, HT, TH, TT).
Q3. A dice is rolled. The probability of getting a prime number is:
- 1/6
- 1/2 ✓ (correct)
- 2/3
- 1/3
Explanation: Prime numbers on a dice are 2, 3, 5. So probability = 3/6 = 1/2.
Q4. If P(A) = 0.3 and P(B) = 0.4, and A and B are independent events, then P(A and B) =
- 0.7
- 0.1
- 0.12 ✓ (correct)
- 0.34
Explanation: For independent events, P(A and B) = P(A) x P(B) = 0.3 x 0.4 = 0.12.
Q5. From a standard deck of 52 cards, the probability of drawing a red card is:
- 1/52
- 1/4
- 1/26
- 1/2 ✓ (correct)
Explanation: There are 26 red cards (13 hearts and 13 diamonds) in a deck of 52, so probability = 26/52 = 1/2.
Q6. The probability of an event plus the probability of its complement equals:
- 1 ✓ (correct)
- 1/2
- 2
- 0
Explanation: P(A) + P(A complement) = 1 for any event A.
Q7. If a bag contains 3 red balls and 2 blue balls, the probability of drawing a red ball is:
- 2/5
- 3/5 ✓ (correct)
- 1/5
- 4/5
Explanation: Probability = (Favorable outcomes) / (Total outcomes) = 3 / (3 + 2) = 3/5.
Q8. Two dice are rolled. The probability of getting a sum of 7 is:
- 1/18
- 1/36
- 1/6 ✓ (correct)
- 1/12
Explanation: Favorable outcomes for sum 7: (1,6), (2,5), (3,4), (4,3), (5,2), (6,1) = 6 outcomes. Total = 36. Probability = 6/36 = 1/6.
Q9. The probability of getting a number greater than 3 when rolling a dice is:
- 1/3
- 1/6
- 2/3
- 1/2 ✓ (correct)
Explanation: Numbers greater than 3 on a dice are 4, 5, 6. So probability = 3/6 = 1/2.
Q10. If P(A) = 0.2 and P(B) = 0.5, and P(A or B) = 0.6, then events A and B are:
- Independent ✓ (correct)
- Dependent
- Mutually exclusive
- Cannot be determined
Explanation: Using P(A or B) = P(A) + P(B) - P(A and B): 0.6 = 0.2 + 0.5 - P(A and B), so P(A and B) = 0.1 = 0.2 x 0.5, confirming independence.
Frequently Asked Questions
What is the difference between theoretical and experimental probability?
Theoretical probability is calculated using mathematical reasoning, while experimental probability is based on actual observations or experiments.
How do you find the probability of independent events?
For independent events, the probability of both occurring is the product of their individual probabilities: P(A and B) = P(A) x P(B).
More Class 10 Mathematics MCQs
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