Question

A card is drawn at random from a pack of 52 cards. Find the probability that the card drawn is not an ace

Answer 1

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

  Let E₁₁ = event of drawing a card which is not an ace
    Then

\[\bar{{E_{11}}}\] = event of drawing an ace card
     There are four aces in a pack of 52 cards, out of which one ace can be drawn in ⁴C₁ways.

\[i . e . n\left( E_{11} \right) = 4\]

\[\therefore P\left( E_{11} \right) = \frac{n\left( E_{11} \right)}{n\left( S \right)} = \frac{1}{13}\]

\[\text{ Hence } , P\left( E_{11} \right) = 1 - P\left( E_{11} \right)\]

\[= 1 - \frac{1}{13} = \frac{12}{13}\]