A-LevelMathematicsProbability and statistics9709/53 · Oct/Nov 2020 · Q25 Marks
An ordinary fair die is thrown until a 6 is obtained. Two ordinary fair dice are thrown together until a pair of 6s is obtained. The number of throws taken is denoted by the random variable X.
- (a)Find the probability that obtaining a 6 takes more than 8 throws.[2]
- (b)Find the expected value of X.[1]
- (c)Find the probability that obtaining a pair of 6s takes either 10 or 11 throws.[2]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2020). The mark or mark type is shown in brackets.
- [M1] p⁸, 0<p<1, no x, + or -
- [A1] 0.233
- [B1] 36
- [M1] OE, unsimplified expression in form p⁹q+p¹⁰q, p+q = 1, no x
- [A1] 0.0425
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