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प्रश्न
A coin is tossed three times. If events A and B are defined as A = Two heads come, B = Last should be head. Then, A and B are ______.
विकल्प
independent
dependent
both
mutually exclusive
उत्तर
A coin is tossed three times. If events A and B are defined as A = Two heads come, B = Last should be head. Then, A and B are dependent.
Explanation:
\[S = \left[ \left( HHH \right), \left( HHT \right), \left( HTH \right), \left( HTT \right), \left( THH \right), \left( THT \right), \left( TTH \right), \left( TTT \right) \right]\]
\[P\left( A \right) = P\left( 2 \text{ heads
}\right) = \frac{3}{8}\]
\[P\left( B \right) = P\left( \text{ last one is head } \right) = \frac{4}{8}\]
\[P\left( A \cap B \right) = \frac{2}{8} = \frac{1}{4} \neq P\left( A \right) P\left( B \right)\]
\[\text{ Thus, A and B are dependent } .\]
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