Question

Two cards are drawn at random and without replacement from a pack of 52 playing cards. Find the probability that both the cards are black.

Answer 1

There are 26 black cards in a pack of 52 cards.

Required probability =P (E and F) = P(E) P(F)

Where, E first card drawn is black, F second card drawn is black

P(E)=$\frac{Totalnumberoffavourableoutcomes}{Totalnumberofoutcomes}=\frac{26}{52}=\frac{1}{2}$
P(F)$\frac{25}{51}$ (After drawing one black, there will be 25 black cards)

$\therefore$ Required probability $P(E\cap F)=P\left(E\right)P\left(F\right)=\frac{1}{2}\times \frac{25}{51}=\frac{25}{102}$