Mathematics 9709 · AS & A Level · Sampling and estimation
Sampling and estimation — practice question
Box $A$ has $8$ white balls and $2$ yellow balls, whereas box $B$ has $5$ white balls and $x$ yellow balls. One ball is selected at random from box $A$ and transferred into box $B$. A ball is then selected at random from box $B$. The tree diagram shows the possible colours of the balls selected.
(i)[1]
Justify the probability $\frac{x}{x+6}$ from the tree diagram.
(ii)[4]
Copy the tree diagram, then complete it.
(iii)[2]
If the ball taken from box $A$ is white, then the chance that the ball chosen from box $B$ is also white is $\frac{1}{3}$. Show that the value of $x$ is $12$.
(iv)[4]
If the ball selected from box $B$ is yellow, find the conditional probability that the ball selected from box $A$ was yellow.
Worked solution & mark scheme
This 11-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Reasonable explanation: the number of balls in $B$ is $5 + x + 1 = x + 6$, so $P(Y)=\frac{x}{x+6}$” …