Question

please i need your help
Application of counting
Two cards are drawn at random from an ordinary deck of 52 cards (no jokers). Find the probability that the 2-card hand contains the given card.
b.No less than 1 diamond.
@kropot72

Answer 1

The probablity of 1 diamond in the two-card hand is:
\[P(1\ \diamond)=\frac{13C1\times39C1}{52C2}=\frac{13\times39\times2}{52\times51}\]
The probablity of 2 diamonds in the two-card hand is:
\[P(2\ diamonds)=\frac{13C2}{52C2}=\frac{13\times12}{52\times51}\]
The required probability is:
P(1 diamond) + P(2 diamonds)= you can calculate