| Exam Board | Pre-U |
|---|---|
| Module | Pre-U 9794/3 (Pre-U Mathematics Paper 3) |
| Year | 2012 |
| Session | June |
| Marks | 6 |
| Topic | Combinations & Selection |
| Type | Basic committee/group selection |
| Difficulty | Easy -1.2 Part (i) is a direct application of combinations formula C(18,4) requiring only recall. Parts (ii) and (iii) are straightforward expected value (5% of 100) and binomial probability calculations with clearly stated parameters. All three parts are routine textbook exercises with no problem-solving or insight required, making this easier than average. |
| Spec | 2.04b Binomial distribution: as model B(n,p)2.04c Calculate binomial probabilities5.01a Permutations and combinations: evaluate probabilities |
**(i)** Recognise combination problem — M1
Obtain 3060 — A1 [2]
**(ii)** Obtain 5 — B1 [1]
**(iii)** State or imply Bin(20, 0.05) — B1
Attempt $P(X < 5)$ via cumulative tables or $P(X = 0) + P(X = 1) + \ldots + P(X = 4)$ — M1
Obtain 0.997(4) — A1 [3]
**Total: [6]**
*"1 – this" gets M0A0*4 In one department of a firm, four employees are selected for promotion from a staff of eighteen.\\
(i) In how many ways can four employees be selected?
It is known that throughout the firm 5\% of those selected for promotion decline it.\\
(ii) If 100 employees are randomly selected for promotion in the firm, calculate the number expected to decline promotion.\\
(iii) If 20 employees are selected at random for promotion, use the binomial distribution to find the probability that fewer than five employees will decline promotion.
\hfill \mbox{\textit{Pre-U Pre-U 9794/3 2012 Q4 [6]}}