Question

A standard deck of 52 cards has four queens. two cards are randomly drawn in succession, without replacement, from a standard deck. what is the probability that the first card is a queen? what is the probability that the second card is a queen?

Answer 1

There are a total of 4 queens in a standard deck of 52 cards. The probability that the 2 consecutive draws are queen is:

Probability = (4 / 52) * (3 / 51)

Probability = 12 / 2652 = 0.004

Answer 2

The probability is the ratio of the number of queens to the total number of cards in a deck. However, when there is no replacement, you subtract 1 from the numerator and denominator.

So, for the first queen, the probability is:
P = 4/52 = 1/13

Now, for the second queen, the available cards are only 51 since 1 was already chosen. Similarly, there are only 3 queens left. Thus, the probability of getting a second queen is:
P = (4/52)(3/51) = 1/221