An urn contains 7 green and 5 yellow balls

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Solution

Q.
An urn contains 7 green and 5 yellow balls. Two balls are drawn at a time. The probability that both balls are of the same colour is

1 $\frac{1}{33}$

2 $\frac{5}{33}$

3 $\frac{7}{22}$

4 $\frac{31}{66}$

Ans.
(4)

$Reqd. prob. = \frac{{}^{7}C_{2}}{{}^{12}C_{2}} + \frac{{}^{5}C_{2}}{{}^{12}C_{2}} = \frac{21 + 10}{66} = \frac{31}{66}$

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