Question

A card is drawn at random from a pack of 52 cards. Find the probability that the card drawn is neither a heart nor a king

Answer 1

Let S denote the sample space.
Then, n(S) = 52

 Let E₅ = event of drawing neither a heart nor a king
   Then

\[\bar{{E_5}}\]  = event of drawing either a heart or a king
     There are 13 cards of heart including one king. Also, there are 3 more kings.
     Therefore, out of these 16 cards, one can draw either a heart or a king in ¹⁶C₁ ways.

\[i . e . n\left( \bar{{E_5}} \right) = 16\]

\[\therefore P\left( \bar{{E_5}} \right) = \frac{n\left( \bar{{E_5}} \right)}{n\left( S \right)} = \frac{16}{52} = \frac{4}{13}\]

\[\therefore P\left( E_5 \right) = 1 - P\left( \bar{{E_5}} \right)\]

\[= 1 - \frac{4}{13} = \frac{9}{13}\]