Probability: experimental probability — KCSE Mathematics

KCSE Mathematics · 108 practice questions · 3 syllabus objectives

36 easy36 medium36 hard

What You'll Learn

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

Perform simple experiments (tossing a coin, rolling a die) to collect relative frequency data; state the relationship between relative frequency and theoretical probability

Explain that as the number of trials increases, experimental probability approaches theoretical probability (law of large numbers)

Probability: experimental probability

Sample Questions

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1
easySHORT ANSWER4 marks

In a game, a player rolls a fair die 120 times and records the results: 1 - 20 times, 2 - 25 times, 3 - 30 times, 4 - 15 times, 5 - 20 times, 6 - 10 times. (a) Calculate the experimental probability of rolling a 3. [2 marks] (b) If the player rolls the die 300 more times, estimate the number of times a 3 is expected to appear. [2 marks]

View Marking Scheme
Part (a) — 2 marks
P(3) = 30/120 or 0.25 stated correctly (1 mk)
Experimental probability of rolling a 3 = 0.25 (1 mk)
Part (b) — 2 marks
P(3) = 0.25 used correctly (1 mk)
Estimated number for next rolls = 0.25 × 300 = 75 stated correctly (1 mk)
2
easySHORT ANSWER4 marks

During an experiment, a student flips a coin 80 times and records 45 heads and 35 tails. (a) Calculate the experimental probability of getting heads. [2 marks] (b) If the student flips the coin 40 more times, how many heads would you expect to get? [2 marks]

View Marking Scheme
Part (a) — 2 marks
P(heads) = 45/80 simplified to 9/16 or 0.5625 (1 mk)
State the probability correctly as a fraction or decimal (1 mk)
Part (b) — 2 marks
P(heads) = 45/80 calculated as 0.5625 (1 mk)
Expected heads in 40 rolls = 0.5625 × 40 = 22.5 or 22 or 23 depending on rounding (1 mk)
3
easySHORT ANSWER4 marks

A student rolls a six-sided die 60 times and records the results as follows: 10 ones, 15 twos, 12 threes, 8 fours, 9 fives, and 6 sixes. (a) Calculate the experimental probability of rolling a three. [2 marks] (b) How many times would you expect to roll a five if the die is rolled 100 more times? [2 marks]

View Marking Scheme
Part (a) — 2 marks
P(three) = 12/60 simplified to 1/5 or 0.2 (1 mk)
State the probability correctly as a fraction or decimal (1 mk)
Part (b) — 2 marks
P(five) = 9/60 calculated as 0.15 (1 mk)
Expected fives in 100 rolls = 0.15 × 100 = 15 (1 mk)
4

A bag contains 5 red balls, 3 blue balls, and 2 green balls. A ball is drawn at random 40 times, resulting in 16 red, 12 blue, and 12 green balls. (a) State the experimental probability of drawing a red ball. (b) If another 80 draws are made, estimate the number of blue balls expected to be drawn. (3 marks)

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