Question

Two cards are drawn from a well shuffled pack of playing cards. Calculate the probability of the

events (i) there is one card of black suits and other of red suits, (ii) both the card are aces (iii)

both the cards are hearts

Answer 1

i)

In a standard deck there are 26 red suits and 26 black suits. After the first pick there is no replacement thus

$$P(1\ red\ \& \ 1\ black)=\dfrac{26}{52}\cdot\dfrac{26}{51}=\dfrac{13}{51}\approx0.2549$$

ii)

In a standard deck there are 4 aces thus

$$P(both\ 2\ aces)=\dfrac{4}{52}\cdot\dfrac{3}{51}=\dfrac{1}{221}\approx0.0045$$

iii)

In a standard deck there are 13 hearts

$$P(both\ 2\ hearts)=\dfrac{13}{52}\cdot\dfrac{12}{51}=\dfrac{1}{17}\approx0.0588$$