Question

You are given a standard deck of 52 cards. Three cards are chosen at random with replacement. What is the probability of choosing an ace, a spade, and a four?

Answer 1

Answer:

0.0288 = 2.88%

Step-by-step explanation:

First we need to know that in one standard deck of 52 cards we have 13 ace cards, 13 spade cards, and 4 four cards.

If we want a combination of ace, spade and four, we calculate the probability of each one, and then multiply them all:

The probability of getting an ace is 13/52 = 1/4

The probability of getting a spade is 13/52 = 1/4

The probability of getting a four is 4/52 = 1/13

As the order of our three cards doesn't matter, we have 3! (factorial of three) = 6 different ways of having a group of ace, spade and four, so our total probability will be multiplied by 6.

So, our probability is:

(1/4) * (1/4) * (1/13) * 6 = 6/208 = 3/104 = 0.0288 = 2.88%

Answer 2

Answer:

Probability = 0.23

Step-by-step explanation:

Probability of picking it choosen those at random without replacement =Pr(ace) + Pr(spade)+Pr(a four)

Probability = 4/52 + 4/52 + 4/52

Probability= 3(4/52)

Probability = 0.23