What is the probability of drawing at least one blue ball in the two draws?

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Multiple Choice

What is the probability of drawing at least one blue ball in the two draws?

Explanation:
The event is easiest to handle by using the complement: probability of no blue in both draws. If the urn has 2 blue and 5 non-blue balls (7 total), then the chance the first draw is not blue is 5/7, and given that, the chance the second draw is not blue is 4/6. Multiply: 5/7 × 4/6 = 20/42 = 10/21. So the probability of drawing at least one blue is 1 − 10/21 = 11/21. You can also add the separate scenarios: blue on the first draw is 2/7, or not blue first and blue second is (5/7)×(2/6) = 10/42 = 5/21; total 2/7 + 5/21 = 11/21.

The event is easiest to handle by using the complement: probability of no blue in both draws. If the urn has 2 blue and 5 non-blue balls (7 total), then the chance the first draw is not blue is 5/7, and given that, the chance the second draw is not blue is 4/6. Multiply: 5/7 × 4/6 = 20/42 = 10/21. So the probability of drawing at least one blue is 1 − 10/21 = 11/21. You can also add the separate scenarios: blue on the first draw is 2/7, or not blue first and blue second is (5/7)×(2/6) = 10/42 = 5/21; total 2/7 + 5/21 = 11/21.

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