(i)[3]
Show that the probability of getting exactly $1$ head and $2$ tails is $\frac{13}{36}$.
(ii)[4]
Construct the probability distribution table for the number of heads obtained.
(iii)[2]
Find the expectation for the number of heads obtained.
Mathematics 9709 · AS & A Level · Linear combinations of random variables
Linear combinations of random variables — practice question
Coin $A$ has been weighted so that the probability of a head is $\frac{2}{3}$. Coin $B$ has been weighted so that the probability of a head is $\frac{1}{4}$. Coin $A$ is tossed twice and coin $B$ is tossed once.
Worked solution & mark scheme
This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Apply either $P(H)=\frac23, P(T)=\frac13$ or $P(H)=\frac14, P(T)=\frac34$, but keep the choice consistent” …
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