Mathematics Class 10 - Probability Notes

Probability

Welcome to the chapter on Probability for Class 10. In this chapter, you will learn what probability is, how to calculate it, and how it is used to predict the chance of events happening. By the end of this chapter, you will be able to solve problems related to probability and understand its applications in real life.

Key Concepts

• Experiment: An action or process that leads to one or more outcomes.
• Outcome: A possible result of an experiment.
• Event: One or more outcomes of an experiment.
• Sample Space: The set of all possible outcomes.
• Probability: The measure of the chance that an event will occur.

What is Probability?

Probability is a number that tells us how likely an event is to happen. It is always between 0 and 1.

• Probability of an impossible event = 0
• Probability of a sure event = 1

Formula for Probability

If all outcomes are equally likely, then:

Probability of an event (E) = Number of favourable outcomes / Total number of possible outcomes

P(E) = n(E) / n(S)
where n(E) = number of favourable outcomes, n(S) = total number of outcomes in the sample space.

Examples

• Tossing a coin: Sample space = {Head, Tail}. Probability of getting a Head = 1/2.
• Throwing a die: Sample space = {1, 2, 3, 4, 5, 6}. Probability of getting a 4 = 1/6.
• Picking a red ball from a bag with 3 red and 2 blue balls: Probability = 3/5.

Properties of Probability

• The probability of any event lies between 0 and 1.
• Sum of probabilities of all possible outcomes = 1.
• If E and F are two events, then P(E or F) = P(E) + P(F) if E and F are mutually exclusive.

Applications of Probability

• Games of chance (cards, dice, coins)
• Weather forecasting
• Insurance and risk assessment
• Predicting outcomes in real life

Practice Questions

1. What is the probability of getting a 5 when a die is thrown?
2. A bag contains 4 green and 6 yellow balls. What is the probability of picking a green ball?
3. If a coin is tossed once, what is the probability of getting a tail?
4. What is the probability of getting an even number when a die is thrown?
5. If a card is drawn from a deck of 52 cards, what is the probability of getting a king?

Challenge Yourself

• A box contains 5 red, 3 blue, and 2 white balls. What is the probability of picking a blue or white ball?
• If two coins are tossed together, what is the probability of getting at least one head?

Did You Know?

• Probability is used in weather reports to predict rain or sunshine!
• The word "probability" comes from the Latin word "probabilis," meaning "likely."

Glossary

• Experiment: An action with uncertain results.
• Outcome: The result of an experiment.
• Event: One or more outcomes.
• Sample Space: All possible outcomes.
• Mutually Exclusive: Events that cannot happen at the same time.

Answers to Practice Questions

1. 1/6
2. 4/10 or 2/5
3. 1/2
4. 3/6 or 1/2 (even numbers: 2, 4, 6)
5. 4/52 or 1/13 (there are 4 kings in a deck)

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Practice probability problems to understand chance and make better predictions!