i.
There are 8 apples in total. Since 5 are red, the probability of getting a red apple is 5/8.
Then, after one red apple is eaten, there are 7 apples in total, and 4 are red, so the probability of getting the second red apple is 4/7.
The final probability is given by the product of each probability:
[tex]P=\frac{5}{8}\cdot\frac{4}{7}=\frac{5}{14}[/tex]
ii.
In order to get apples of different colours, there are two cases: first red and second green, or first green and second red.
The probability of the first case is:
[tex]\frac{5}{8}\cdot\frac{3}{7}=\frac{15}{56}[/tex]
The probability of the second case is:
[tex]\frac{3}{8}\cdot\frac{5}{7}=\frac{15}{56}[/tex]
Adding the probabilities, we have:
[tex]P=\frac{15}{56}+\frac{15}{56}=\frac{30}{56}=\frac{15}{28}[/tex]
