Question

There are 3 sets of balls numbered 1 through 11 placed in a bowl. If 3 balls are randomly chosen without replacement, find the probability that the balls have the same number. Express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth.

Answer 1

The probability that the balls have the same number is 1/165 or approximately 0.00606.

Step-by-step explanation:

To find the probability that the balls have the same number, we need to consider the number of favorable outcomes and the total number of possible outcomes.

1. Number of favorable outcomes: Since there are 11 balls and each ball has a unique number, there is only 1 way to choose 3 balls with the same number.
2. Total number of possible outcomes: The total number of ways to choose 3 balls from the 11 balls without replacement is given by the combination formula: C(11,3) = 165.

Therefore, the probability is given by:

Probability = Number of favorable outcomes / Total number of possible outcomes = 1 / 165 = 0.00606 (rounded to the nearest millionth).