Probability Solved Examples (Class 10 Maths)
Probability measures the likelihood of an event happening. It ranges from 0 (impossible) to 1 (certain). Understanding probability helps make informed deci
TL;DR: Probability measures the likelihood of an event happening. It ranges from 0 (impossible) to 1 (certain). Understanding probability helps make informed…
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Probability measures the likelihood of an event happening. It ranges from 0 (impossible) to 1 (certain). Understanding probability helps make informed deci
Probability — Solved Numerical Examples (Step by Step)
Example 1: A die is rolled once. Find the probability of getting a number greater than 4.
Solution: When a die is rolled, the possible outcomes are: 1, 2, 3, 4, 5, 6
Total number of outcomes = 6
Favorable outcomes (numbers greater than 4): 5, 6
Number of favorable outcomes = 2
Using the formula: P(event) = Number of favorable outcomes / Total number of outcomes
P(number > 4) = 2 / 6 = 1 / 3
Example 2: A card is drawn from a standard deck of 52 cards. What is the probability of drawing a red card?
Solution: Total number of cards in a deck = 52
Number of red cards (hearts + diamonds) = 26
Using the formula: P(event) = Number of favorable outcomes / Total number of outcomes
P(red card) = 26 / 52 = 1 / 2 = 0.5
Example 3: Two fair coins are tossed. Find the probability of getting at least one head.
Solution: When two coins are tossed, the possible outcomes are: HH, HT, TH, TT
Total number of outcomes = 4
Favorable outcomes (at least one head): HH, HT, TH
Number of favorable outcomes = 3
P(at least one head) = 3 / 4
Example 4: A bag contains 5 red balls and 3 blue balls. If one ball is drawn at random, what is the probability of drawing a red ball?
Solution: Total number of balls = 5 + 3 = 8
Number of red balls = 5
P(red ball) = Number of red balls / Total number of balls
P(red ball) = 5 / 8
Example 5: Find the probability of getting a sum of 7 when two dice are rolled.
Solution: When two dice are rolled, total number of outcomes = 6 × 6 = 36
Favorable outcomes (sum = 7):
(1,6), (2,5), (3,4), (4,3), (5,2), (6,1)
Number of favorable outcomes = 6
P(sum = 7) = 6 / 36 = 1 / 6
Example 6: The probability of an event happening is 0.3. Find the probability of the event not happening.
Solution: Given: P(event) = 0.3
Using the formula: P(event not happening) = 1 - P(event)
P(not happening) = 1 - 0.3
P(not happening) = 0.7
Example 7: A number is chosen at random from the numbers 1 to 20. What is the probability that it is a multiple of 5?
Solution: Numbers from 1 to 20: 1, 2, 3, ..., 20
Total outcomes = 20
Multiples of 5 from 1 to 20: 5, 10, 15, 20
Number of favorable outcomes = 4
P(multiple of 5) = 4 / 20 = 1 / 5
Tips
- Probability always ranges from 0 to 1. An event with probability 0 is impossible, and an event with probability 1 is certain. Probabilities can be expressed as fractions, decimals, or percentages.
- The sum of probabilities of all possible outcomes in an experiment is always 1. This means P(event) + P(not event) = 1.
- When finding probability of compound events (two or more things happening), carefully count all favorable outcomes by listing them systematically or using permutations and combinations.
Frequently Asked Questions
What is the difference between theoretical and experimental probability?
Theoretical probability is calculated based on the assumption that all outcomes are equally likely. It is calculated as (favorable outcomes) / (total outcomes). Experimental probability is based on actual experiments or past data: (number of times event occurred) / (total number of trials).
If two events are independent, how do I find the probability of both occurring?
For independent events, the probability of both events occurring is the product of their individual probabilities: P(A and B) = P(A) × P(B). For example, if P(A) = 0.5 and P(B) = 0.3, then P(A and B) = 0.5 × 0.3 = 0.15.
More Maths Solved Examples
- Quadratic Equations
- Trigonometry
- Arithmetic Progressions
- Surface Areas and Volumes
- Coordinate Geometry
- Polynomials
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