O-LevelMathematicsProbability4024/22 · May/June 2014 · Q45 Marks

A bag contains six identical balls numbered 2, 3, 4, 5, 6 and 7.

(a)(i)A ball is taken from the bag at random. Find, as a fraction in its lowest terms, the probability that the number on the ball is a multiple of 3,[1]
(a)(ii)prime.[1]
(b)(i)All six balls are replaced in the bag. Two balls are taken from the bag, one after the other, without replacement. The numbers on the two balls are added together. Complete this possibility diagram to show all the outcomes. [Diagram of addition table][1]
(b)(ii)(a)Find the probability that the sum of the numbers is odd,[1]
(b)(ii)(b)less than 8.[1]

This question uses a diagram from the original paper, which isn't shown here. Open the full paper from the past papers archive to see it.

Mark scheme

Marking points from the official mark scheme (May/June 2014). The mark or mark type is shown in brackets.

[1] (a)(i) 1/3
[1] (a)(ii) 2/3
[1] (a)(ii) After 0+0 allow B1 for 2/6 and 4/6 Or 0.33 and 0.66 or better
[1] (b)(i) 25 numbers completed correctly
[1] (b)(ii)(a) 18/30 oe isw
[1] (b)(ii)(b) 8/30 oe isw
[1] (b)(ii)(b) After 0+0+0 for (b), If all 36 used B1 for 18/36 and 10/36 If 35 used, B1 for 18/35 and 9/35

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