A-LevelMathematicsProbability and statistics9709/52 · Oct/Nov 2020 · Q27 Marks
A bag contains 5 red balls and 3 blue balls. Sadie takes 3 balls at random from the bag, without replacement. The random variable X represents the number of red balls that she takes.
- (a)Show that the probability that Sadie takes exactly 1 red ball is 15/56.[2]
- (b)Draw up the probability distribution table for X.[3]
- (c)Given that E(X) = 15/8, find Var(X).[2]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2020). The mark or mark type is shown in brackets.
- [M1] (5C1 × 3C2) / 8C3 or (5/8) × (3/7) × (2/6) × 3
- [A1] AG, WWW
- [B1] Probability distribution table with correct outcomes with at least one probability less than 1, allow extra outcome values if probability of zero stated.
- [B1] 2 of P(0), P(2) and P(3) correct
- [B1 FT] 4th probability correct or FT sum of 3 or more probabilities = 1, with P(1) correct
- [M1] Substitute their attempts at scores in correct variance formula, must have ' - mean²' (FT if mean calculated) (condone probabilities not summing to 1 for this mark)
- [A1]
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