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1. An urn contains 2 red, 3 green and 2 blue balls. If 2 balls are drawn at random, find the probability that no ball is blue.

A. $\frac{5}{7}$

B. $\frac{10}{21}$

C. $\frac{2}{7}$

D. $\frac{11}{21}$

Solution:

Total number of balls = (2 + 3 + 2) = 7
Let, E be the event of drawing 2 non-blue balls.
Then, n (E) =

^{5} C_{4} = \frac{5 \times 4}{2 \times 1}

= 10
And, n (S) =

^{7} C_{2} = \frac{7 \times 6}{2 \times 1}

= 21

∴ P (E) = \frac{n (E)}{n (S)} = \frac{10}{21}

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