MRSM Trial 2025 Add Maths Paper 2, Question 9Probability Distribution

Solved on video in English · Form 5, Probability Distribution · 8:43 video

The question

(a)(i)

(a) A study in a country found that 40% of youths choose to be self-employed. If 9 youths are randomly selected, find the probability that: (i) none of the youths choose to be self-employed.

(a)(ii)

If 9 youths are randomly selected, find the probability that: (ii) at least 2 youths choose not to be self-employed.

(b)(i)

(b) A worker must arrive at his office before 0800 hours every day to receive a free breakfast pack. The time taken to travel from his house to his office is normally distributed with a mean of 40 minutes and a standard deviation of 8 minutes. (i) If he departs from his house at 0725 hours, find the probability that he will not receive the free breakfast pack.

(b)(ii)

(b) The time to travel to the office is normally distributed with mean 40 minutes and standard deviation 8 minutes; he must arrive before 0800 to get the free breakfast pack. (ii) If he departs at 0710 hours every day, calculate the number of days he will receive the free breakfast pack within 300 working days.

MRSM Trial 2025 Add Maths Paper 2, Question 9: the question as drawn in Eduly's video8:43

Part (a)(i)

Step 1

Model X = number self-employed as X ~ B(9, 0.4), using P(X = r) = ⁹Cᵣ (0.4)ʳ (0.6)⁹⁻ʳ.

Why this step

Each youth is an independent yes/no trial, and we count how many say yes, so it's binomial. X counts self-employed, so p = 0.4, not 0.6.

1 more step, with the reason for it, in the full solution

Final answer

0.01008

Where students lose marks

Watch out: X counts the self-employed, so p = 0.4, not 0.6. Then evaluate (0.6)⁹ carefully on your calculator.

Part (a)(ii)

3 more steps, each with the reason for it, in the full solution

Final answer

0.9962

Where students lose marks

Watch out: 'not self-employed' means p = 0.6, and 'at least 2' needs both P(Y = 0) and P(Y = 1) taken from 1.

Part (b)(i)

3 more steps, each with the reason for it, in the full solution

Final answer

0.734

Where students lose marks

Watch out: he misses the pack when travel time is at least 35 min, so we need the upper tail P(Z ≥ −0.625).

Part (b)(ii)

2 more steps, each with the reason for it, in the full solution

Final answer

268 days

Where students lose marks

Watch out: 0710 gives 50 minutes, not 35, and remember to multiply the probability 0.8944 by 300 days.

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