Question

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

Answer 1

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

 Let E₇ = event of drawing neither an ace nor a king
        Then

\[\bar{{E_7}}\] = event of drawing either an ace or a king
       There are four ace cards and four king cards.
       Therefore, out of these 8 cards, one can draw either an ace or a king in ⁸C₁ ways.

\[i . e . n\left( \bar{{E_7}} \right) = 8\]

\[\therefore P\left( \bar{{E_7}} \right) = \frac{n\left( \bar{{E_7}} \right)}{n\left( S \right)} = \frac{8}{52} = \frac{2}{13}\]

\[\therefore P\left( E_7 \right) = 1 - P\left( \bar{{E_7}} \right)\]

\[= 1 - \frac{2}{13} = \frac{11}{13}\]