A-LevelMathematicsProbability and statistics9709/53 · May/June 2021 · Q46 Marks
Three fair six-sided dice, each with faces marked 1, 2, 3, 4, 5, 6, are thrown at the same time, repeatedly. For a single throw of the three dice, the score is the sum of the numbers on the top faces.
- (a)Find the probability that the score is 4 on a single throw of the three dice.[3]
- (b)Find the probability that a score of 18 is obtained for the first time on the 5th throw of the three dice.[3]
Mark scheme
Marking points from the official mark scheme (May/June 2021). The mark or mark type is shown in brackets.
- [3] M1 (1/6)³ ×k, where k is an integer.
- M1 Multiply a probability by 3, not +, – or ÷
- A1 Accept 3/216 or 1/72 or 0.0138 or 0.0139
- [3] B1 P(18)=([1/6]³)=1/216
- M1 (1-p)⁴p, 0 < their p < 1
- A1 0.00454
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