When charles randomly chooses a fruit from a basket of apples and oranges, the odds are 5 to 3 that he will select an orange. what is the probability that he chooses 2 oranges, if fruits are not replaced?

The probability that he chooses 2 oranges is:

The odds of choosing a orange from a basket is:

If  O denote orange

and T denote the total number of fruits

Then the odds of selecting an orange is given by:

This means that:

The total number of fruits in basket i.e. T=8

so that the ratio matches.

Hence, the probability of getting orange in first draw= 5/8

Now , the second draw is independent of first and the fruits are not replaced.

This means now we have to choose fruits from remaining 7 fruits in the basket .

Probability of getting orange in second draw is: 4/7

Hence, the probability of choosing 2 oranges if the fruits are not replaced is:

9x