A) \[\frac{9}{11}\]
B) \[\frac{4}{7}\]
C) \[\frac{32}{37}\]
D) \[\frac{31}{66}\]
E) \[\frac{35}{66}\]
Correct Answer: D
Solution :
Let n(S) be the sample space. Then, n(S) = number of ways of drawing 2 balls out \[(7+5)=12\]is \[{{\,}^{12}}{{C}_{2}}=\frac{11\times 12}{2}=66\] Let n be the event of getting both balls of the same colour. Then, n = number of ways of drawing (2 balls out of 7) or (2 balls out of \[\therefore \]\[n(E)={{\,}^{7}}{{C}_{2}}+{{\,}^{5}}{{C}_{2}}=\frac{7\times 6}{2}+\frac{5\times 4}{2}=21+10=31\] \[\therefore \]\[P(E)=\frac{n(E)}{n(S)}=\frac{31}{66}\]
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