A bag contains 11 oranges, four of which are damaged. Two oranges are selected at random without replacement. The probability that both oranges are not damaged is:

Answer 1

To find the probability that both oranges are not damaged, we need to calculate the probability of selecting one undamaged orange and then selecting another undamaged orange from the remaining oranges.

There are 11 oranges in total, 4 of which are damaged. So, there are 11 - 4 = <<11-4=7>>7 undamaged oranges.

The probability of selecting an undamaged orange on the first draw is 7/11.

Once one undamaged orange is selected, there are 10 remaining oranges in total, including 6 undamaged oranges. So, the probability of selecting an undamaged orange on the second draw is 6/10.

To find the probability of both events happening, we multiply the probabilities: (7/11) * (6/10) = 42/110.

Therefore, the probability that both oranges are not damaged is 42/110 or 0.3818 (rounded to four decimal places).