A-LevelMathematicsProbability and statistics9709/53 · May/June 2023 · Q14 Marks
Two fair coins are thrown at the same time repeatedly until a pair of heads is obtained. The number of throws taken is denoted by the random variable X.
- (a)State the value of E(X).[1]
- (b)Find the probability that exactly 5 throws are required to obtain a pair of heads.[1]
- (c)Find the probability that fewer than 7 throws are required to obtain a pair of heads.[2]
Mark scheme
Marking points from the official mark scheme (May/June 2023). The mark or mark type is shown in brackets.
- [B1] P(HH) = [E(X) =] 4
- [B1] [P(X=5)=(3/4)^4 (1/4)=] 0.0791
- [M1] 1-p^n, 0 < p < 1, n = 6, 7
- [M1] or p+p(1-p)+p(1-p)² +...+p(1-p)^n, where n = 4, 5.
- [A1] Accept 0.82202148... to at least 3SF.
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