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Question
Mark the correct alternative in the following question:
Two dice are thrown. If it is known that the sum of the numbers on the dice was less than 6, then the probability of getting a sum 3, is
Options
\[\frac{1}{18}\]
\[ \frac{5}{18}\]
\[ \frac{1}{5}\]
\[ \frac{2}{5}\]
Solution
\[\text{ Let } : \]
\[\text{ A be the event of getting a sum of 3 and } \]
\[\text{ B be the event of getting a sum of 6 } \]
\[\text{ As } , A = \left\{ \left( 1, 2 \right), \left( 2, 1 \right) \right\} \text{ and } B = \left\{ \left( 1, 1 \right), \left( 1, 2 \right), \left( 1, 3 \right), \left( 1, 4 \right), \left( 2, 1 \right), \left( 2, 2 \right), \left( 2, 3 \right), \left( 3, 1 \right), \left( 3, 2 \right), \left( 4, 1 \right) \right\}\]
\[\text{ So } , n\left( A \right) = 2, n\left( B \right) = 10 \text{ and } n\left( A \cap B \right) = n\left( A \right) = 2\]
\[\text{ Now } , \]
\[P\left( A|B \right) = \frac{n\left( A \cap B \right)}{n\left( B \right)}\]
\[ = \frac{2}{10}\]
\[ = \frac{1}{5}\]
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