Mathematics 9709 · AS & A Level · Discrete random variables

Discrete random variables — practice question

A pair of fair coins is tossed over and over until a pair of tails appears. The random variable $X$ represents the number of throws needed to obtain a pair of tails.
(a)[1]

Calculate the expected value of $X$.

(b)[1]

Calculate the probability that exactly 3 throws are needed to obtain a pair of tails.

(c)[2]

Calculate the probability that fewer than 6 throws are needed to obtain a pair of tails.

(d)[5]

At another time, a pair of fair coins is tossed 80 times. Use an approximation to calculate the probability that a pair of tails occurs more than 25 times.

Worked solution & mark scheme

This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Correct evaluation gives $\dfrac{1}{1/4}=4$.” …

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