O-LevelMathematicsProbability4024/22 · May/June 2021 · Q119 Marks
A bag contains 12 balls. There are x black balls in the bag and the other balls are white. Two balls are taken at random from the bag without replacement.
- (a)Complete the tree diagram. [Figure 11.A][2]
- (b)Find an expression for the probability of taking one ball of each colour. Write your answer as a single fraction in terms of x.[3]
- (c)The probability that both balls are black is 14/33. Form an equation in x and solve it to find the number of black balls in the bag. Show your working.[4]
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Mark scheme
Marking points from the official mark scheme (May/June 2021). The mark or mark type is shown in brackets.
- [2] (a) x/12, (x-1)/11, (12-x)/12, (12-x-1)/11 (11-x)/11 oe correctly placed B1 for one correct
- [3] (b) x(12-x)/66 oe simplified single fraction final answer M2 for x/12 * (12-x)/11 + (12-x)/12 * x/11 or M1 for x/12 * (12-x)/11 or (12-x)/12 * x/11
- [4] (c) x/12 * (x-1)/11 = 14/33 M1 x² - x - 56 = 0 oe A1 Alternative: x(x - 1) = 56 cao (x – 8)(x + 7) [= 0] or M1 Dep on M1 [x =] -(-1) + √(-1)² - 4×1×-56 / 2×1 FT factorisation/use of formula for their 3-term quadratic Alternative: 8(8-1) = 56 soi
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