SPM 2024 Add Maths Paper 1, Question 12Probability Distribution

Solved on video in English and Bahasa Melayu · Form 5, Probability Distribution · 5:21 video

The question

(a)

Diagram 9 shows six letter cards used in a Binomial experiment: C, E, R, D, I, K. A card will be chosen randomly in each Bernoulli trial. The card is then replaced. (a) If there are 120 trials, find the expected value of the number of consonant letter cards that will be chosen.

(b)

Using the same six letter cards C, E, R, D, I, K and the same Bernoulli experiment as part (a), (b) if there are 5 trials, find the probability that the number of consonant letter cards chosen is more than the number of vowel letter cards chosen.

Part (a)

Step 1

Identify the consonants: C, R, D, K — that is 4 consonants out of 6 cards.

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

Final answer

Expected value = 80

Where students lose marks

Watch out: p is the chance of a consonant (4/6 = 2/3), not a vowel (2/6). Using 1/3 gives 40, not 80.

Part (b)

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

Final answer

P(X ≥ 3) = 64/81 (≈ 0.7901)

Where students lose marks

Watch out: include P(X = 5). If you use the complement, subtract P(X = 0), P(X = 1) and P(X = 2) from 1.

Watch every step of this question solved on video (5:21), with the reason behind each step and a box that checks your own answer.

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