O-LevelMathematicsProbability4024/12 · May/June 2014 · Q214 Marks
Luis has 3 black pens and 7 red pens in a case. He takes two pens from the case at random without replacement.
- (a)Complete the tree diagram to show the possible outcomes and their probabilities. First pen Second pen black / 2⁄9 / ----------- black (3⁄10) / / \ \ [BLANK for probability] ----------- red \ \ [BLANK for probability] black [BLANK for probability] red[1]
- (b)(i)Find, as a fraction in its lowest terms, the probability that Luis takes two black pens,[1]
- (b)(ii)Luis takes two different coloured pens.[2]
Mark scheme
Marking points from the official mark scheme (May/June 2014). The mark or mark type is shown in brackets.
- [1] 7⁄10, 3⁄9, 6⁄9, 7⁄9 correctly completed
- [1] 1⁄15
- [2] 7⁄15 FT
- [2] B1 for 21⁄90 oe FT
- [2] Or M1 for (3⁄10 × 7⁄9) + (7⁄10 × 3⁄9)
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