Probability: combined events — KCSE Mathematics

KCSE Mathematics · 104 practice questions · 4 syllabus objectives

34 easy36 medium34 hard

What You'll Learn

Key learning outcomes for this topic, aligned to the KNEC KCSE syllabus.

Apply the addition rule P(A ∪ B) = P(A) + P(B) – P(A ∩ B) for any two events; simplify for mutually exclusive events

Apply the multiplication rule P(A ∩ B) = P(A) × P(B|A) for dependent events and P(A) × P(B) for independent events

Use tree diagrams and two-way tables to represent and calculate probabilities for two-stage and three-stage experiments

Probability: combined events

Sample Questions

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1
easySHORT ANSWER3 marks

A bag contains 3 red balls and 2 blue balls. If one ball is drawn at random and not replaced, calculate the probability of drawing a red ball first and then a blue ball. (3 marks)

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Part (a) — 3 marks
Probability of drawing a red ball first is 3/5 (1 mk)
After drawing a red ball, there are now 4 balls left (1 mk)
Probability of drawing a blue ball next is 2/4 or 1/2, so overall probability is (3/5) * (1/2) = 3/10 (1 mk)
2
easySHORT ANSWER4 marks

In a class, the probability that a student studies Mathematics is 0.6. If a student studies Mathematics, the probability that they also study Physics is 0.8. Calculate the probability that a randomly selected student studies both Mathematics and Physics. (4 marks)

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Part (a) — 4 marks
Apply the multiplication rule: P(M ∩ P) = P(M) × P(P|M) (1 mk)
Substitute values: P(M ∩ P) = 0.6 × 0.8 (1 mk)
Calculate: P(M ∩ P) = 0.48 (1 mk)
State the final answer as 0.48 (1 mk)
3
easySHORT ANSWER3 marks

A box contains 5 red balls and 3 blue balls. If a red ball is drawn first and not replaced, find the probability of drawing a blue ball second. (3 marks)

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Part (a) — 3 marks
Total balls after first draw = 7 (4 red + 3 blue) (1 mk)
P(blue) = 3/7 after a red ball is drawn first (1 mk)
Correct probability stated as 3/7 (1 mk)
4

In a class, the probability that a student studies mathematics is 0.6 and the probability that the same student studies physics is 0.4. If the probability that a student studies both subjects is 0.2, calculate the probability that a randomly selected student studies either mathematics or physics. (4 marks)

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