Question

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

Answer 1

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

Let E₉ = event of not drawing a diamond card
   Then

\[\bar{{E_9}}\]= event of drawing a diamond card
      There are 13 diamond cards in a pack of 52 cards, out of which one diamond card can be drawn in ¹³C₁

\[i . e . n\left( \bar{{E_9}} \right) = \frac{13}{52} = \frac{1}{4}\]

\[\therefore P\left( E_9 \right) = 1 - P\left( E_9 \right)\]

\[= 1 - \frac{1}{4} = \frac{3}{4}\]