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The Mathematics of Maybe: Introduction to Probability – Class 9 Mathematics notes, important questions and MCQs

NCERT Class 9 Mathematics, chapter 7. Notes, key terms, important questions with answers and MCQs.

Chapter overview

Probability measures chance. Experimental probability comes from repeated trials; theoretical probability comes from equally likely outcomes.

Experimental probability

P(E) = number of trials in which E happened / total number of trials.
More trials give a value closer to the theoretical one.
Example: a coin tossed 100 times shows 46 heads → P(head) = 0.46.

Theoretical probability

P(E) = favourable outcomes / total equally likely outcomes.
0 ≤ P(E) ≤ 1; impossible = 0, certain = 1.
P(E) + P(not E) = 1.

Key terms

Trial: one performance of an experiment
Outcome: a possible result of a trial
Equally likely: outcomes with the same chance

Formulas

P(E) = favourable / total
P(not E) = 1 − P(E)

Important questions with answers

A coin is tossed 500 times and shows heads 285 times. Find the experimental probability of tails.2 marks

Tails = 500 − 285 = 215. P(tails) = 215/500 = 0.43.

A bag has 4 red, 5 blue and 6 green balls. One ball is drawn at random. Find P(blue) and P(not green).3 marks

Total = 15. P(blue) = 5/15 = 1/3. P(not green) = (15 − 6)/15 = 9/15 = 3/5.

In 1000 families with 2 children: 2 girls in 205, 1 girl in 515, no girl in 280. Find the probability of each case, check that they add to 1, and explain the difference between experimental and theoretical probability.5 marks

P(2 girls) = 0.205, P(1 girl) = 0.515, P(0 girls) = 0.280; sum = 1.000 ✓. Experimental probability is based on observed results of actual trials and can change with more trials. Theoretical probability is calculated from equally likely outcomes (here BB, BG, GB, GG gives 1/4, 1/2, 1/4). As the number of trials grows, experimental values tend to come closer to theoretical values.

Quick revision

Probability ranges from 0 to 1.
Sum of probabilities of all outcomes = 1.
Die has 6 outcomes; coin has 2.

Exam tips

In experimental questions, use the counts given in the table, not theory.
Probability is written as a fraction, decimal or percentage — never above 1.

Practice MCQs

Probability of an impossible event is
1. 0
2. 1
3. 0.5
4. −1
Show answer
Answer: (a) 0. It never happens.
A die is rolled. P(getting 4) is
1. 1/6
2. 1/4
3. 4/6
4. 1/2
Show answer
Answer: (a) 1/6. One favourable out of six.
Which value can be a probability?
1. 1.2
2. −0.3
3. 3/2
4. 0.8
Show answer
Answer: (d) 0.8. It must be between 0 and 1.
A coin tossed 200 times gave 110 heads. Experimental P(tail) is
1. 0.55
2. 0.9
3. 0.5
4. 0.45
Show answer
Answer: (d) 0.45. 90/200 = 0.45.
P(E) = 0.3. P(not E) =
1. 0.3
2. 0.03
3. 1.3
4. 0.7
Show answer
Answer: (d) 0.7. 1 − 0.3.
A bag has 3 red and 5 blue balls. P(red) =
1. 3/5
2. 1/3
3. 5/8
4. 3/8
Show answer
Answer: (d) 3/8. 3 out of 8.
In 50 throws of a die, 6 appeared 12 times. Experimental P(not 6) is
1. 0.24
2. 0.12
3. 0.76
4. 0.88
Show answer
Answer: (c) 0.76. 38/50 = 0.76.
A spinner has 8 equal parts numbered 1–8. P(a number greater than 5) =
1. 1/8
2. 5/8
3. 1/2
4. 3/8
Show answer
Answer: (d) 3/8. 6, 7, 8: 3/8.

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Written by Kundali IQ from standard, well-established facts to help with revision. This is not an official NCERT publication; always read your textbook too.