Answer to Question #125811 in Statistics and Probability for Adnan

Question

Two cards are drawn from a well shuffled pack of 52 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

Solution

i) there is one card of black suits and other of red suits,

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

p(b & r) = p(b)*p(r) = 26/52 * 26/51 =0.2549

(ii) both the card are aces

in a standard deck there are 4 aces thus

p( a & a) = P(a) *p(a) = 4/52*3/51 =0.0045

(iii)both the cards are hearts

in a standard deck there are 13 hearts

p( h & h) = 13/52*12/51= 0.0588