Question

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 ______.

Options

• independent

• dependent

• both

•  mutually exclusive

Answer 1

 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:

\[S = \left[ \left( HHH \right), \left( HHT \right), \left( HTH \right), \left( HTT \right), \left( THH \right), \left( THT \right), \left( TTH \right), \left( TTT \right) \right]\]

\[P\left( A \right) = P\left( 2 \text{ heads
}\right) = \frac{3}{8}\]

\[P\left( B \right) = P\left( \text{ last one is head }  \right) = \frac{4}{8}\]

\[P\left( A \cap B \right) = \frac{2}{8} = \frac{1}{4} \neq P\left( A \right) P\left( B \right)\]

\[\text{ Thus, A and B are dependent } .\]