Probability and Statistics for Class 10: A Complete Guide to Mastering the Basics

Probability and Statistics are two scoring and practical chapters in Class 10 Maths. Learn them well, and you can gain marks easily. This guide explains the basics in simple words. It also gives solved examples, practice questions, and a quick revision sheet.

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What is Probability? (Class 10)

Probability tells us how likely an event is to happen.
We use it to predict outcomes. For example: coin toss, dice roll, or drawing a card.

Formula (Class 10):

$$P(E) = \frac{\text{Number of favourable outcomes}}{\text{Total number of outcomes}}$$

P(E)=Total number of outcomesNumber of favourable outcomes​

Note: Probability is always between 0 and 1.
0 means impossible. 1 means certain.

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Easy Probability Examples

Example 1 — Dice (Basic)
Question: What is the probability of rolling a 5 on a fair six-sided dice?
Solution: Favourable outcomes = 1. Total outcomes = 6.

$$P = \frac{1}{6}$$

P=61​

Example 2 — Coin (Basic)
Question: What is the probability of getting a Head when you toss a coin?
Solution: Favourable = 1. Total = 2.

$$P = \frac{1}{2}$$

P=21​

Example 3 — Cards (Tricky)
Question: What is the probability of drawing a red ace from a 52-card deck?
Solution: Red aces = 2 (hearts, diamonds). Total = 52.

$$P = \frac{2}{52} = \frac{1}{26}$$

P=522​=261​

Tip: Always count outcomes carefully. Write them down if needed.

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What is Statistics? (Class 10)

Statistics helps us collect, organise, and interpret numerical data.
In Class 10 you mainly learn:

• Mean (average)

• Median (middle value)

• Mode (most frequent value)

These tools help us understand data from surveys, tests, and experiments.

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Key Statistics Formulas

Mean (Ungrouped data):

$$\text{Mean} = \frac{\sum x}{n}$$

Mean=n∑x​

Median:

• If n is odd → middle value.

• If n is even → average of the two middle values.

Mode:

• The number that appears most often.

Mean (Grouped data):

$$\bar{x} = \frac{\sum f_i x_i}{\sum f_i}$$

xˉ=∑fi​∑fi​xi​​

(Where

$x_i$

xi​ = class midpoint and

$f_i$

fi​ = frequency)

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Solved Statistics Examples

Example 1 — Mean (Basic)
Data: 6, 12, 18, 24
Sum = 60, n = 4
Mean = 60 ÷ 4 = 15

Example 2 — Median (Basic)
Data: 3, 8, 9, 15, 17 → Middle value = 9 → Median = 9

Example 3 — Mode (Basic)
Data: 4, 4, 5, 6, 6, 6, 7 → Mode = 6

Example 4 — Mean (Grouped — Tricky)

Compute

$\sum f_i x_i = 2×5 + 3×15 + 5×25 = 10 + 45 + 125 = 180$

∑fi​xi​=2×5+3×15+5×25=10+45+125=180
Total frequency = 10

Mean = 180 ÷ 10 = 18

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Common Mistakes to Avoid

• Not arranging data before finding median.

• Mixing up favourable and total outcomes in probability.

• Skipping steps; lose method marks.

• Wrong midpoint for grouped data.

• Not checking totals in frequency tables.

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Practice Questions (Try These)

Probability

1. A bag has 4 red and 6 blue balls. Find the probability of picking a blue ball.

2. Two coins are tossed. What is the probability of exactly one head?

3. Pick a letter from “MATHEMATICS”. Find the probability of getting a vowel.

Statistics

1. Find the mean: 12, 18, 20, 25, 30.

2. Find the median: 7, 3, 9, 1, 4.

3. Find the mode: 2, 2, 4, 4, 4, 6, 8.

4. For grouped data: (0–5:3), (5–10:5), (10–15:2) — find the mean.

(Answers available on request or in class notes.)

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Quick Revision Sheet

Probability:

$P(E) = \dfrac{\text{favourable}}{\text{total}}$

P(E)=totalfavourable​
Mean (ungrouped):

$\dfrac{\Sigma x}{n}$

nΣx​
Median: Middle value (if even, average of two middles)
Mode: Most frequent value

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How to Study These Topics Fast

• Read the concept. Then practice 5–10 questions daily.

• Start with basic problems. Move to tricky ones later.

• Always write steps clearly. Teachers give method marks.

• Use past year papers for board-style questions.

• Review mistakes and fix the weak spots.

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