Question

Een Shot 2022- -0319 P2. Adrian has a box with 5 red and 3 green apples in it. He takes out an apple at random and eats it. He then takes out another apple at random and also eats it.a Find the probability that he eatsi two red applesii two apples of different colours.

Answer 1

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:

`P=(5)/(8)\cdot(4)/(7)=(5)/(14)`

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:

`(5)/(8)\cdot(3)/(7)=(15)/(56)`

The probability of the second case is:

`(3)/(8)\cdot(5)/(7)=(15)/(56)`

Adding the probabilities, we have:

`P=(15)/(56)+(15)/(56)=(30)/(56)=(15)/(28)`