(a)[2]
Show that, in this case, $P(B)=\frac{7}{16}$.
(b)[2]
Find the value of $P(A\mid B)$.
(c)[3]
The random variable $X$ counts how many heads Eric gets when he throws the three coins. Draw up the probability distribution table for $X$.
Mathematics 9709 · AS & A Level · Discrete random variables
Discrete random variables — practice question
Eric has three coins. One coin is fair, while each of the other two is biased so that the chance of getting a head on any throw is $\frac{1}{4}$, independently of every other throw. Eric throws all three coins at the same time. Events $A$ and $B$ are defined below.
$A$: all three coins show matching outcomes
$B$: at least one of the biased coins shows a head
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