O-LevelMathematicsProbability4024/21 · Oct/Nov 2022 · Q59 Marks

[Figure 5.1] George has two bags each containing black balls and white balls.

(a)(i)George says: I am more likely to take a black ball from bag 2 than from bag 1. Show that George is correct.[2]
(a)(ii)George takes a ball at random from Bag 2, notes its colour and replaces it. He repeats this 220 times. How many times would he expect to take a white ball?[2]
(b)(i)A bag contains 7 blue counters, 6 red counters and 3 green counters. Yasmin takes two counters from the bag at random without replacement. Complete the tree diagram.[2]
(b)(ii)Find the probability that at least one of the counters is red.[3]

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Mark scheme

Marking points from the official mark scheme (Oct/Nov 2022). The mark or mark type is shown in brackets.

[2] (a)(i) Correct justification with probabilities 0.44... and 0.45... seen; B1 for 4/9 oe or 5/11 oe seen
[2] (a)(ii) 120; M1 for 6/11 x 220
[2] (b)(i) Correct tree diagram; M1 for 4 or more probabilities completed correctly
[3] (b)(ii) 5/8 oe nfww; M2FT for 1 - (10/16 × 9/15) oe or M1FT for (6/16 × 7/15) + (6/16 × 3/15) + (7/16 × 6/15) + (3/16 × 6/15) + (6/16 × 5/15) oe

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