Question

4

cards are drawn from a standard deck without replacement. What is the probability that at least one of the cards drawn is a diamond? Express your answer as a fraction or a decimal number rounded to four decimal places.

Answer 1

the probability that at least one of the cards drawn is a diamond is 5/32

Explanation:

In a standard 52-card deck, there are 13 diamond cards,

Now,

The probability of a card being a diamond is ,

P = 13/52

P = 1/4

Now, we have to find the probability that atleast one of the 4 cards is a diamond, we calculate the probabilities,

There is 1 diamond in the 4 cards,

Hence the other 3 are not diamonds i.e the porbability for not being a diamond is,

N = 1-1/4 = 3/4

So,

The total probability is,

T1 = (3/4)(3/4)(3/4)(1/4)

T1 = 27/256

There are 2 diamonds in the 4 cards,

And the other 2 are not diamonds, we get,

T2 = (1/4)(1/4)(3/4)(3/4)

T2=9/256

There are 3 diamonds in the 4 cards,

and 1 is not,

T3 = (1/4)(1/4)(1/4)(3/4)

T3 = 3/256

ALL FOUR are diamonds,

T4 = (1/4)(1/4)(1/4)(1/4)

T4 = 1/256

Hence, the probability that at least 1 is a diamond is,

T = T1 + T2 + T3 + T4

T = (27/256) + (9/256) + (3/256) + (1/256)

T = 40/256

T = 5/32

Answer 2

`(1)/(4)`