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Question
Mark the correct alternative in the following question:A flash light has 8 batteries out of which 3 are dead. If two batteries are selected without replacement and tested, then the probability that both are dead is
Options
\[ \frac{3}{28}\]
\[ \frac{1}{14}\]
\[\frac{9}{64} \]
\[\frac{33}{56}\]
Solution
\[\text{ We have } , \]
\[\text{ The total number of batteries } = 8\]
\[\text{ The number of dead batteries }= 3\]
\[\text{ Let A be the event of selecting the first dead battery and } \]
\[\text{ B be the event of selecting the second dead battery } \]
\[\text{ Now } , \]
\[P\left( \text{ both dead batteries are selected } \right) = P\left( A \cap B \right)\]
\[ = P\left( A \right) \times P\left( B|A \right)\]
\[ = \frac{3}{8} \times \frac{2}{7}\]
\[ = \frac{3}{28}\]
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