(a)[1]
Show that the probability of obtaining a score of 4 is $\frac{1}{12}$.
(b)[1]
Find the mean value of $X$.
(c)[1]
Find the probability that a score of 4 is first obtained on the 6th throw.
(d)[2]
Find the value of $P(X < 8)$.
Mathematics 9709 · AS & A Level · Discrete random variables
Discrete random variables — practice question
For two fair six-sided dice, the score is the total of the numbers showing on the top faces. The dice are rolled again and again until a score of 4 is obtained. Let the random variable $X$ denote the number of throws needed.
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This 5-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Probability of scoring 4 found as $\frac{3}{36}=\frac{1}{12}$” …
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