A bag contains 2 red, 3 green and 2 blue balls. Two balls are drawn at random. What is the probability that none of the balls drawn is blue?

10 21
11 21
2 7
5 7

Correct answer: 10 21

Solution

There are 5 non-blue balls (2 red + 3 green) out of 7 total balls. The number of ways to draw 2 non-blue balls is \(\binom{5}{2}\), and total ways are \(\binom{7}{2}\). Thus probability = \(\frac{\binom{5}{2}}{\binom{7}{2}} = \frac{10}{21}\).

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