65) Suppose 3 of a dozen oranges are bruised and 2 are chosen at random from the dozen.The probability that both are bruised is: 1/22 1/11 o 1/6 o 1/4 o 1/3 o x No Answer Selected

To solve this problem, we need to find the probability of choosing 2 bruised oranges out of the 3 bruised oranges in the dozen.

Given information:
- There are 3 bruised oranges out of a dozen (12 oranges).
- 2 oranges are chosen at random from the dozen.

Step 1: Find the probability of choosing the first bruised orange.
Probability of choosing the first bruised orange = Number of bruised oranges / Total number of oranges
Probability of choosing the first bruised orange = 3 / 12 = 1/4

Step 2: Find the probability of choosing the second bruised orange.
After choosing the first bruised orange, there are 2 bruised oranges left and 11 oranges in total.
Probability of choosing the second bruised orange = Number of bruised oranges left / Total number of oranges left
Probability of choosing the second bruised orange = 2 / 11

Step 3: Find the probability of choosing both bruised oranges.
Probability of choosing both bruised oranges = Probability of choosing the first bruised orange × Probability of choosing the second bruised orange
Probability of choosing both bruised oranges = (1/4) × (2/11) = 2/44 = 1/22

Therefore, the probability that both oranges chosen are bruised is 1/22.

The correct answer is: $$1/22$$