A-LevelMathematicsProbability and statistics9709/51 · May/June 2020 · Q15 Marks
The score when two fair six-sided dice are thrown is the sum of the two numbers on the upper faces.
- (a)Show that the probability that the score is 4 is 1/12.[1]
- (b)The two dice are thrown repeatedly until a score of 4 is obtained. The number of throws taken is denoted by the random variable X. Find the mean of X.[1]
- (c)Find the probability that a score of 4 is first obtained on the 6th throw.[1]
- (d)Find P(X < 8).[2]
Mark scheme
Marking points from the official mark scheme (May/June 2020). The mark or mark type is shown in brackets.
- [1] Prob of 4 (from 1,3, 3,1 or 2,2) = 3/36 = 1/12 AG
- [1] Mean = 1/(1/12) = 12
- [1] (11/12)^5 x 1/12 = 0.0539 or 161051/2985984
- [1] 1 - (11/12)^7
- [1] 0.456 or 16344637/35831808
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