Box $A$ has $6$ red balls and $4$ blue balls. Box $B$ has $x$ red balls and $9$ blue balls. A ball is picked at random from box $A$ and put into box $B$. A ball is then picked at random from box $B$.
(a)[3]
Complete the tree diagram below by writing the four missing probabilities in terms of $x$.
(b)[2]
Show that the probability that both balls selected are blue is $\dfrac{4}{x+10}$.
(c)[5]
It is given that the probability of both balls chosen being blue is $\dfrac{1}{6}$. Find the probability, correct to $3$ significant figures, that the ball chosen from box $A$ is red given that the ball chosen from box $B$ is red.
Worked solution & mark scheme
This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: “A correctly placed probability shown in the right place on the tree diagram, for example $\frac{x+1}{x+10}$.” …