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A bowl contains 15 green balls numbered consecutively 1 through 15 and 13 white balls numbered consecutively?
1 through 13. I want to select 5 balls at random without replacement. Find the probability that both green ball number 1 and white ball number 1 are selected. Use 3 decimal places for your answer
There are 15+13 = 28 balls total. Thus, there are 28C5 = 98280 ways to choose 5 balls.
Now, the number of ways to pick green #1 and white #1. If we've chosen the two 1's, we don't care what the other three balls are. There are 26 balls left, and 26C3 = 2600 ways to choose them. Thus, the probability is:
2600/98280 = 5/189 ≈ 0.026455 ≈ 2.646%
EDIT: note that other answers that say things like "1/15" or "1 out of 13" are not correct, because we are not picking from two separate bowls containing just green and just white. They are all mixed together in one bowl. It is possible to get all 5 green or all 5 white. Also, Dana is on the right track, but forgot to take into consideration there are many ways to pick the other three balls if you have chosen the two #1 balls.
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