A) \[\frac{10}{21}\]
B) \[\frac{11}{21}\]
C) \[\frac{2}{7}\]
D) \[\frac{5}{7}\]
E) None of these
Correct Answer: A
Solution :
Explanation Option [a] is correct. Total number of balls \[=\left( 2+3+2 \right)=7\] Let S be the sample space. Then, n (S) = Number of ways of drawing 2 balls out of \[7{{\,}^{7}}{{C}_{2}}\] \[\frac{(7\times 6)}{(2\times 1)}=21\] Let E = Event of drawing 2 balls, none of which is blue. \[\therefore \] n = Number of ways of drawing 2 balls out of (2+3) balls \[={{\,}^{5}}{{C}_{2}}=\frac{(5\times 4)}{2\times 1}=10\] \[\therefore \,\,\,P(E)\,=\frac{n(E)}{n(S)}=\frac{10}{21}.\]
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