A) \[\frac{5}{17}\]
B) \[\frac{12}{17}\]
C) \[\frac{17}{30}\]
D) \[\frac{3}{5}\]
Correct Answer: B
Solution :
We define the following events : \[{{A}_{1}}:\] Selecting a pair of consecutive letter from the word LONDON. \[{{A}_{2}}:\] Selecting a pair of consecutive letters from the word CLIFTON. E : Selecting a pair of letters ?ON?. Then \[P({{A}_{1}}\cap E)=\frac{2}{5};\] as there are 5 pairs of consecutive letters out of which 2 are ON. \[P({{A}_{2}}\cap E)=\frac{1}{6};\] as there are 6 pairs of consecutive letters of which one is ON. \ The required probability is \[P\left( \frac{{{A}_{1}}}{E} \right)\]\[=\frac{P({{A}_{1}}\cap E)}{P({{A}_{1}}\cap E)+P({{A}_{2}}\cap E)}=\frac{\frac{2}{5}}{\frac{2}{5}+\frac{1}{6}}=\frac{12}{17}.\]
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