(a)[4]
John plays two games of squash. The chance that he wins his first game is $0.3$. If he wins his first game, the chance that he wins his second game is $0.6$. If he loses his first game, the chance that he wins his second game is $0.15$. Given that he wins his second game, find the probability that he won his first game.
(b)[4]
Jack has a pack of $15$ cards. $10$ cards show a robot and $5$ cards show an aeroplane. Emma has a pack of cards. $7$ cards show a robot and $x - 3$ cards show an aeroplane. One card is chosen at random from Jack’s pack and one card is chosen at random from Emma’s pack. The probability that both cards show robots is $\frac{7}{18}$. Write an equation in terms of $x$ and hence find the value of $x$.