Data Handling & Probability (VI–VIII) • Topic 4 of 4

Introduction to Probability

Class 8 gives children their first formal taste of probability, and CTET keeps it strictly elementary — coins, dice, marbles and spinners. The core formula is P(event) = (number of favourable outcomes) ÷ (total number of equally likely outcomes). Every probability is a number from 0 to 1: an impossible event has probability 0, a certain event has probability 1, and you can never get a value above 1 — a frequent CTET 'spot the wrong answer' trap. The probabilities of an event and its complement add to 1, so P(not E) = 1 − P(E). Standard sample spaces to know cold: a coin has 2 outcomes (head, tail); a single die has 6 outcomes (1–6), of which 3 are even and 3 are odd, and {2, 3, 5} are prime. CTET also distinguishes theoretical probability (from equally likely outcomes) from experimental probability (favourable trials ÷ total trials actually performed) — and the pedagogy point that real experiments only approach the theoretical value as the number of trials grows. Children's errors to recognise: giving a probability greater than 1, counting outcomes that are not equally likely, and confusing 'favourable' with 'total'.

✅ Solved examples

1. A bag holds 5 red and 3 green balls. One ball is drawn at random. What is the probability that it is green?
Favourable (green) = 3. Total balls = 5 + 3 = 8. P(green) = 3/8.
2. A fair die is rolled once. What is the probability of getting an even number?
Even numbers on a die are 2, 4, 6 → 3 favourable outcomes. Total outcomes = 6. P(even) = 3/6 = 1/2.
3. A child claims the probability of an event is 1.4. Explain why this must be wrong.
Probability always lies between 0 and 1 inclusive (0 ≤ P ≤ 1). A value of 1.4 is greater than 1, which is impossible — at most an event can be certain, with probability exactly 1. The child has likely confused probability with a count or a percentage error.
4. If the probability that it rains tomorrow is 0.3, what is the probability that it does NOT rain?
P(not rain) = 1 − P(rain) = 1 − 0.3 = 0.7, since an event and its complement have probabilities that add to 1.

✏️ Practice — try these, take hints as needed

1. A fair coin is tossed once. What is the probability of getting a head?
A coin has 2 equally likely outcomes.
One of them is favourable.
1/2
2. A die is rolled. What is the probability of getting a number greater than 4?
Numbers greater than 4 are 5 and 6.
That is 2 out of 6 outcomes.
2/6 = 1/3
3. What is the probability of an event that is certain to happen?
Certain means it always occurs.
It is the maximum value probability can take.
1
4. A box has 4 white and 6 black pens. One pen is picked at random. What is the probability it is white?
Favourable = 4 white.
Total = 4 + 6 = 10.
4/10 = 2/5

📝 Topic test — 8 questions

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