1

A bag contains $5$ green and $3$ yellow sweets. Two sweets are taken at random without replacement. Work out the probability that the two sweets are the same colour. [4]

2

In a game you play two rounds. The probability of winning the first round is $\dfrac{2}{3}$. If you win the first round, the probability of winning the second is $\dfrac{1}{2}$; if you lose the first, the probability of winning the second is $\dfrac{1}{4}$. Work out the probability that you win exactly one of the two rounds. [4]

3

It rains on any given day with probability $\dfrac{1}{5}$, independently of other days. Work out the probability that it rains on at least one of the next two days. [3]

4

A biased coin lands on heads with probability $p$. It is flipped twice. The probability of getting two heads is $\dfrac{9}{25}$. Work out the probability of getting two tails. [4]

5

A bag contains $n$ red counters and $4$ blue counters. Two counters are taken at random without replacement. The probability that both counters are blue is $\dfrac{1}{6}$. Work out the value of $n$. [5]