Question

A card is drawn from a pack of 52 cards so the teach card is equally likely to be selected. In which of the following cases are the events A and B independent? 

B = the card drawn is a spade, B = the card drawn in an ace.

Answer 1

\[P\left( \text{ spade }\right) = P\left( A \right) = \frac{13}{52} = \frac{1}{4}\]
\[P\left( \text{ ace }  \right) = P\left( B \right) = \frac{4}{52} = \frac{1}{13}\]
\[P\left( A \cap B \right) = P\left( \text{ ace of spade } \right) = \frac{1}{52}\]
\[P\left( A \cap B \right) = P\left( A \right) P\left( B \right)\]
\[\text{ Thus, A and B are independent events } .\]