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Question

The fruit basket at a summer camp contained 4 oranges and 5 apples. Carlos chose 1 piece of fruit at random from the basket and gave the fruit to his friend Duncan. Then Carlos reached in again and chose another piece of fruit at random for himself.



What is the probability that Duncan received an orange and that Carlos then received an apple? Express your answer in simplest form.

Answer 1

The probability of picking an orange on the first pick is 4/9, since there are 4 oranges and 9 pieces of fruit all together.

 

If an orange is taken on the first pick, there are then 8 pieces of fruit left, of which 5 are apples.  So the probability of picking an apple on the second pick, if an orange was picked on the first, would be 5/8.

 

So the probability of both happening is 4/9 * 5/8 = 5/18