Example 5: HSC 2001 paper Q 8(b)

Five candidates A,B,C,D and E are standing for election. Their names are drawn randomly.

(i)

What is the probability that A is drawn first? 1 mark

(ii)

What is the probability that the order is A,B,C,D,E? 2 marks

ANSWER

(i)

$$P(A_1) = {{n(A)} \over {n(S)_1}} = {1 \over 5}$$

(ii)

Random sampling means the draws are independent and the sample space is reduced by 1 each time.

$$P(ABCDE) = \frac{1}{5} \times \frac{1}{4} \times \frac{1}{3} \times \frac{1}{2}$$

EXAMINERS' REMARKS, 2001

Question 8

(b)

(i)

Almost all candidates scored this mark.

(ii)

A significant number of candidates failed to understand the method for non-replacement. this type of problem does not lend itself to a tree diagram (far too many branches) and most who attempted one had failed to identify the pattern of choices.