(a)[3]
Show that the chance of getting exactly 2 heads and 1 tail is $\frac{4}{9}$.
(b)[3]
Draw up a probability distribution table for $X$.
(c)[2]
Given that $\text{E}(X) = \frac{32}{15}$, determine $\mathrm{Var}(X)$.
Mathematics 9709 · AS & A Level · Discrete random variables
Discrete random variables — practice question
Each of the three coins $A$, $B$ and $C$ is tossed once. Coins $A$ and $B$ are both biased so that the chance of a head is $\frac{2}{3}$. Coin $C$ is biased so that the chance of a head is $\frac{4}{5}$. The random variable $X$ counts how many heads are obtained when the three coins are tossed.
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