(a)[1]
Show that the probability $P(X = 2)$ equals $\frac{3}{20}$.
(b)[3]
Draw up a probability distribution table for $X$.
(c)[2]
Using $\text{E}(X) = \frac{47}{60}$, find $\mathrm{Var}(X)$.
Mathematics 9709 · AS & A Level · Discrete random variables
Discrete random variables — practice question
Jacob flips three coins at the same time. The first coin is biased so that the probability of getting a head when it is tossed is $\frac{1}{3}$. The second coin is biased so that the probability of getting a head when it is tossed is $\frac{1}{4}$. The third coin is biased so that the probability of getting a head when it is tossed is $\frac{1}{5}$. Let the random variable $X$ represent the total number of heads obtained.
Worked solution & mark scheme
This 6-mark question has a full step-by-step worked solution and mark scheme. One marking point: “A correct probability calculation that gives $\frac{9}{60}=\frac{3}{20}$, with a consistent order of coins.” …
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