A-LevelMathematicsProbability and statistics9709/52 · Oct/Nov 2021 · Q37 Marks
A bag contains 5 yellow and 4 green marbles. Three marbles are selected at random from the bag, without replacement. The random variable X is the number of yellow marbles selected.
- (a)Show that the probability that exactly one of the marbles is yellow is .[3]
- (b)Draw up the probability distribution table for X.[3]
- (c)Find E(X).[1]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2021). The mark or mark type is shown in brackets.
- [M1] a/9 × b/8 × c/7, 0 < a,b,c integers < 5, for one arrangement.
- [M1] Their three-factor probability × 3, 3C1, 3C2 or 3P1, (or repeated adding) no additional terms.
- [A1] AG. Convincingly shown, including identifying possible scenarios, may be on tree diagram WWW.
- [B1] Table with correct X values and one correct probability inserted appropriately. Condone any additional X values if probability stated as 0.
- [B1] Second identified correct probability, may not be in table.
- [B1] All probabilities identified and correct .
- [B1] [E(X) =] 840/504 or 5/3 or 1.67 OE Must be evaluated.
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