Class 10 Maths Probability Notes

4.1 Probability — A Theoretical Approach

Probability is the measure of the likelihood or chance that a particular event will occur. It is a fundamental concept in statistics and is used in various fields like games, weather forecasting, finance, and decision-making.

Probability is calculated using the following formula:$$\text{Probability (P)} = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}}$$Probability (P)=Total number of possible outcomesNumber of favorable outcomes​

Where:

• Favorable outcomes are the outcomes that satisfy the condition or event we are interested in.
• Total possible outcomes are all the possible outcomes that could occur.

The value of probability is always between 0 and 1:

• 0 means the event will never occur.
• 1 means the event will definitely occur.
• A probability of 0.5 means the event is equally likely to occur or not occur.

Example 1: Tossing a Coin

When tossing a coin, the two possible outcomes are Heads (H) or Tails (T).

• The total number of possible outcomes = 2 (H, T).
• If the event is “Getting Heads,” the number of favorable outcomes = 1 (H).

Thus, the probability of getting heads is:$$P(\text{Heads}) = \frac{1}{2}$$P(Heads)=21​

Example 2: Rolling a Die

When rolling a fair six-sided die, the possible outcomes are 1, 2, 3, 4, 5, 6.

• The total number of possible outcomes = 6.
• If the event is “Rolling an even number,” the favorable outcomes are 2, 4, 6. Thus, the number of favorable outcomes = 3.

The probability of rolling an even number is:$$P(\text{Even number}) = \frac{3}{6} = \frac{1}{2}$$P(Even number)=63​=21​

Example 3: Drawing a Card

In a deck of 52 cards, there are 13 cards of each suit (Hearts, Diamonds, Clubs, Spades), and 4 suits in total.

• The total number of possible outcomes = 52 (the total number of cards in the deck).
• If the event is “Drawing a red card,” there are 26 red cards (13 Hearts and 13 Diamonds), which are the favorable outcomes.

Thus, the probability of drawing a red card is:$$P(\text{Red card}) = \frac{26}{52} = \frac{1}{2}$$P(Red card)=5226​=21​

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14.2 Summary

In this chapter, we explored theoretical probability, which provides a way of quantifying how likely an event is to happen, based on equally likely outcomes.

Key points:

1. Probability of an event is a number between 0 and 1.
2. It is calculated as the ratio of favorable outcomes to the total number of outcomes.
3. In many real-world situations, we can apply theoretical probability to predict the likelihood of events such as coin tosses, dice rolls, and drawing cards from a deck.

MCQs Based on the “Probability” Chapter:

1. The probability of an event is:

a) Always greater than 1
b) Always between 0 and 1
c) Always 1
d) Always 0

Answer: b) Always between 0 and 1

2. When a coin is tossed, the probability of getting heads is:

a) 0
b) 1
c) $\frac{1}{2}$21​
d) 1.5

Answer: c) $\frac{1}{2}$21​

3. The total number of possible outcomes when a die is rolled is:

a) 5
b) 6
c) 7
d) 8

Answer: b) 6

4. The probability of drawing a red card from a deck of 52 cards is:

a) $\frac{1}{4}$41​
b) $\frac{1}{2}$21​
c) $\frac{1}{3}$31​
d) $\frac{3}{4}$43​

Answer: b) $\frac{1}{2}$21​

5. The probability of not getting a “6” when rolling a die is:

a) $\frac{5}{6}$65​
b) $\frac{1}{6}$61​
c) $\frac{1}{3}$31​
d) $\frac{1}{2}$21​

Answer: a) $\frac{5}{6}$65​