Further Mathematics Paper 2, May/June. 2012
 Questions: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 Main
Weakness/Remedies
Strength

Question 15

(a)      Two items are selected at random from four items labelled (p, q, r, s).
(i)      List the sample space if sampling is done:
(µ)     with replacement;
(b)     without replacement.

• Find the probability that r is at least one of the two objects selected:

(b)     in a(i) µ;
(c)     in a (i) b.

(b)     How many whole numbers from 100 to 999 are divisible by:
(i)      4;
(ii)      both 3 and 4?

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Observation

It was reported that candidates’ performance in this question was poor.  Majority of the candidates were reported not to have obtained the correct sample spaces in part (a).  They were also not able to differentiate between sample with replacement and without replacement.  The required sample spaces were as tabulated below:

With replacement

 p q r s p p,p p,q p,r p,s q q,q q,q q,r q,s r r,p r,q r,r r,s s s,p s,q s,r s,s

Without Replacement

 p q r s p - p,q p,r p,s q q,p - q,r q,s r r,p r,q - r,s s s,p s,q s,r -