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1. A box contains 10 black and 10 white balls. What is the probability of drawing 2 balls of the same colour ?

A. $\frac{9}{19}$

B. $\frac{9}{38}$

C. $\frac{10}{19}$

D. $\frac{5}{19}$

Solution:

Total number of balls = (10 + 10) = 20
Let E be the event of drawing 2 balls of the same colour.
n (E) = number of ways of drawing 2 black balls or 2 white balls.
n (E) =

(^{10} C_{2} \times^{10} C_{2})

= 2 \times^{10} C_{2}

= 2 \times \frac{10 \times 9}{2 \times 1}

= 90
n (S) = number of ways of drawing 2 balls out of 20 balls

=^{20} C_{2} = \frac{20 \times 19}{2 \times 1}

= 190

∴ P (E) = \frac{n (E)}{n (S)} = \frac{90}{190} = \frac{9}{19}

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