Mathematics 9709 · AS & A Level · Discrete random variables

Discrete random variables — practice question

Two fair coins are tossed together again and again until a pair of heads appears. Let the random variable $X$ stand for the number of tosses needed.
(a)[1]

State the value of $\text{E}(X)$, giving your answer clearly.

(b)[1]

Find the probability that exactly 5 throws are needed to obtain a pair of heads.

(c)[2]

Find the probability that fewer than 7 throws are needed to obtain a pair of heads.

Worked solution & mark scheme

This 4-mark question has a full step-by-step worked solution and mark scheme. One marking point: “The correct value is $P(HH)=\frac14$ or $\text{E}(X)=4$.” …

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