Probability (Case Study) (Class 10 Mathematics)
CBSE case-based probability questions involving real-world scenarios like games, sports, and quality control. Students calculate experimental and theoretic
TL;DR: CBSE case-based probability questions involving real-world scenarios like games, sports, and quality control. Students calculate experimental and theo…
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CBSE case-based probability questions involving real-world scenarios like games, sports, and quality control. Students calculate experimental and theoretic
Probability (Case Study) MCQs with Answers & Explanations
Q1. In a cricket tournament, the probability that Team A wins the next match is 0.6 and Team B wins is 0.4. If they play 3 matches, what is the probability that Team A wins at least 2 matches?
- 0.648 ✓ (correct)
- 0.432
- 0.216
- 0.352
Explanation: P(at least 2 wins) = P(exactly 2) + P(exactly 3). P(exactly 2) = C(3,2) * 0.6^2 * 0.4 = 3 * 0.36 * 0.4 = 0.432. P(exactly 3) = 0.6^3 = 0.216. Total = 0.432 + 0.216 = 0.648.
Q2. A die is rolled twice. What is the probability of getting a sum of 7?
- 1/12
- 1/6 ✓ (correct)
- 1/8
- 5/36
Explanation: Favorable outcomes for sum 7: (1,6), (2,5), (3,4), (4,3), (5,2), (6,1) = 6 outcomes. Total outcomes = 36. P = 6/36 = 1/6.
Q3. In a bag, there are 5 red balls, 3 blue balls, and 2 green balls. If two balls are drawn without replacement, what is the probability that both are red?
- 10/90
- 25/90
- 20/90 ✓ (correct)
- 5/45
Explanation: Without replacement: P(first red) = 5/10 and P(second red) = 4/9. P(both red) = 5/10 x 4/9 = 20/90 = 2/9.
Q4. A quality control inspector finds that 2% of products are defective. If a sample of 100 products is checked, what is the expected number of defective products?
- 10
- 1
- 5
- 2 ✓ (correct)
Explanation: Expected value E = n * p = 100 * 0.02 = 2. This is the mean of a binomial distribution.
Q5. Two events A and B are independent. P(A) = 0.5 and P(B) = 0.6. What is P(A and B)?
- 0.3 ✓ (correct)
- 1.1
- 0.5
- 0.6
Explanation: For independent events, P(A and B) = P(A) * P(B) = 0.5 * 0.6 = 0.3.
Q6. In a lottery, the probability of winning the jackpot is 1/1000000. If 10 million tickets are sold, what is the expected number of jackpot winners?
- 1
- 10 ✓ (correct)
- 100
- 0.01
Explanation: Expected winners = total tickets * probability = 10,000,000 * (1/1,000,000) = 10.
Q7. A student has a 70% chance of passing Math and 80% chance of passing English. Assuming independence, what is the probability of failing both subjects?
- 0.10
- 0.20
- 0.06 ✓ (correct)
- 0.14
Explanation: P(fail Math) = 0.3, P(fail English) = 0.2. P(fail both) = 0.3 * 0.2 = 0.06.
Frequently Asked Questions
What is the difference between theoretical and experimental probability?
Theoretical probability is calculated based on mathematical reasoning without conducting an experiment, using P(A) = (favorable outcomes)/(total outcomes). Experimental probability is determined by actually performing an experiment and recording results, calculated as P(A) = (frequency of occurrence)/(total number of trials). As trials increase, experimental probability approaches theoretical probability (Law of Large Numbers).
When can we use the multiplication rule P(A and B) = P(A) * P(B)?
This formula applies only when events A and B are independent, meaning the occurrence of one event does not affect the probability of the other. For dependent events, we use P(A and B) = P(A) * P(B|A), where P(B|A) is the conditional probability of B given A has occurred. Always verify independence before applying the simpler formula.
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