Question

Out of a deck of 52, what is the probability you draw 4 cards and all four cards are DIAMOND cards? (You can see a deck of cards here.)

a
.0026
b
.00000015
c
.077
d
.25

Answer 1

Answer: Choice A) 0.0026

This decimal value is the approximation of the fraction 11/4165

================================================================

Step-by-step explanation:

There are 13 diamonds out of 52 total.

The probability of getting a diamond card is 13/52.

After selecting that diamond card and not putting it back, we have 13-1 = 12 diamonds left out of 52-1 = 51 left. The probability of getting another diamond is 12/51.

Then the probability of getting a third diamond is 11/50, and finally 10/49 represents the probability of getting a fourth diamond. Each time we need a new probability, we just subtract 1 from the numerator and denominator.

The numerators are: 13, 12, 11, 10

The denominators are: 52, 51, 50, 49

We'll multiply the four fractions to get our final answer

(13/52)*(12/51)*(11/50)*(10/49) = 0.00264105642257

This rounds to 0.0026 which is roughly a 0.26% chance

The answer as an exact fraction is 11/4165