Question

if four cards are selected randomly one after the other from a deck of 52 cards without replacement, what is the probability that the first two are diamonds and the third and fourth are club and spade

Answer 1

Solution:

We have to draw four cards from a pack of 52 cards.

First we have to find probability that first card is diamond.

Total cards = 52

Diamond cards = 13

Probability that first card is diamond is 13/52.

For second card,

Total cards = 51 (we do not replace first card.)

Diamond cards = 12

Probability that second card is diamond = 12/51

For third card,

Total cards = 50

Total number of club cards = 13

Probability that third card is club = 13/50

For fourth card,

Total cards = 49

Total number of spade cards = 13

Probability that fourth card is spade = 13/49

Required probability that the first two are diamonds and the third and fourth are club and spade is given as below:

Required probability = (13/52)*(12/51)*(13/50)*(13/49)

Required probability = 0.004057623