A-LevelMathematicsProbability and statistics9709/53 · Oct/Nov 2021 · Q710 Marks
Box A contains 6 red balls and 4 blue balls. Box B contains x red balls and 9 blue balls. A ball is chosen at random from box A and placed in box B. A ball is then chosen at random from box B.
- (a)Complete the tree diagram below, giving the remaining four probabilities in terms of x. [Figure][3]
- (b)Show that the probability that both balls chosen are blue is 4/(x + 10)[2]
- (c)It is given that the probability that both balls chosen are blue is 1/6. Find the probability, correct to 3 significant figures, that the ball chosen from box A is red given that the ball chosen from box B is red.[5]
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 (Oct/Nov 2021). The mark or mark type is shown in brackets.
- [B1] One probability correct in correct position.
- [B1] Another probability correct in correct position.
- [B1] Other two probabilities correct in correct positions.
- [M1] Method consistent with their tree diagram.
- [A1] AG
- [B1] Find value of x. Can be implied by correct probabilities in calculation.
- [B1FT] 6/10 × their (x+1)/(x+10) as numerator or denominator of fraction.
- [M1] 6/10 × their (x+1)/(x+10) + 4/10 × their x/(x+10) seen anywhere.
- [A1FT] Seen as denominator of fraction.
- [A1] If B0 M0: SC B1 for 3/8 or 0.375 or SC B1 45/73 or 0.616.
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