1

A box contains 4 black and 2 white beads. A bead is taken at random, its colour noted and replaced, then a second is taken. The tree diagram is partly complete. Find the probability marked $?$ (the second pick being white after a black).

2

The probability Priya revises on a given evening is $\dfrac{3}{5}$. If she revises, the probability she passes the weekly quiz is $\dfrac{3}{5}$. If she does not revise, the probability she passes is $\dfrac{1}{2}$. Complete the tree diagram. Use it to find the probability that Priya revises and passes the quiz.

3

A bag contains $n$ orange sweets and 2 lemon sweets. Two sweets are taken at random without replacement. The probability that both sweets are orange is $\dfrac{15}{28}$. Work out the value of $n$.