Alice will play 2 games of tennis against Bob. Alice’s chances of winning each game is 0.7. Work out the probability of Alice winning exactly one match.

The chances of Alice winning a game is 0.7, therefore the chances of Bob winning a game is 0.3. To work out the probability of Alice winning exactly one game, the probabilities of Alice winning once and Bob winning once is calculated (0.70.3=0.21). This is then multiplied by the amount of combinations where Alice wins exactly once (2, since Alice can win either the first or second game).Therefore the answer is: 0.70.3*2=0.42.
(Please note that a tree diagram makes this much easier to explain. I will go through this in the interview)