Probability Solved Examples (Class 10 Mathematics)
Calculate probabilities of simple and compound events using theoretical and empirical approaches. These problems build foundational probability reasoning.
TL;DR: Calculate probabilities of simple and compound events using theoretical and empirical approaches. These problems build foundational probability reason…
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Calculate probabilities of simple and compound events using theoretical and empirical approaches. These problems build foundational probability reasoning.
Probability — Solved Numerical Examples (Step by Step)
Example 1: A die is rolled. What is the probability of getting an even number?
Solution: Total outcomes = 6 (1, 2, 3, 4, 5, 6)
Favorable outcomes (even numbers) = 3 (2, 4, 6)
Probability P(even) = 3/6 = 1/2 = 0.5
Example 2: Two coins are tossed. What is the probability of getting at least one head?
Solution: Total outcomes = 4 (HH, HT, TH, TT)
Favorable outcomes (at least one head) = 3 (HH, HT, TH)
Probability = 3/4 = 0.75
Example 3: A card is drawn from a standard deck of 52 cards. What is the probability of drawing a face card (Jack, Queen, or King)?
Solution: Total cards = 52
Face cards = 3 × 4 = 12 (3 face cards in each of 4 suits)
Probability = 12/52 = 3/13 ≈ 0.23
Example 4: A bag contains 5 red balls and 3 blue balls. One ball is drawn at random. What is the probability that it is red?
Solution: Total balls = 5 + 3 = 8
Red balls = 5
Probability P(red) = 5/8 = 0.625
Example 5: Two dice are rolled. What is the probability of getting a sum of 7?
Solution: Total outcomes = 6 × 6 = 36
Favorable outcomes (sum = 7): (1,6), (2,5), (3,4), (4,3), (5,2), (6,1) = 6 outcomes
Probability = 6/36 = 1/6 ≈ 0.167
Example 6: In a class of 40 students, 25 play cricket and 15 play football. If a student is selected at random, what is the probability that they play cricket?
Solution: Total students = 40
Students playing cricket = 25
Probability = 25/40 = 5/8 = 0.625
Tips
- Probability P(event) = Number of favorable outcomes / Total number of possible outcomes (for equally likely outcomes).
- Probability of an event ranges from 0 to 1; 0 means impossible, 1 means certain.
- For independent events: P(A and B) = P(A) × P(B); for mutually exclusive events: P(A or B) = P(A) + P(B).
Frequently Asked Questions
What is the difference between theoretical and experimental probability?
Theoretical probability is based on logical reasoning and assumptions, while experimental probability is based on actual experiments and observed outcomes.
Can probability be greater than 1?
No, probability is always between 0 and 1 (inclusive). A probability greater than 1 or negative is not valid.
More Mathematics Solved Examples
- Real Numbers (HCF LCM Euclid)
- Pair of Linear Equations in Two Variables
- Circles
- Statistics
- Linear Equations in Two Variables
- Heron's Formula
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