Answer to Question #183537 in Statistics and Probability for Muhammad Haris

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) The standard 52 card deck has 26 red and 26 black cards. The probability that there is one card of black suits and other of red suits is

$\displaystyle P(A) = P(rb) + P(br) = \frac{26}{52} \cdot \frac{26}{51} + \frac{26}{52} \cdot \frac{26}{51} = 0.5098$

ii) There are 4 aces in the card deck. Therefore,

$\displaystyle P(B) = \frac{4}{52} \cdot \frac{3}{51} = 0.0045$

iii) There are 13 hearts. So,

$\displaystyle P(C) = \frac{13}{52} \cdot \frac{12}{51} = 0.0588$