Question

Consider an example of a deck of 52 cards:

What is the probability of drawing three queens from a standard deck of cards, given that the first card drawn was a queen? Assume that the cards are not replaced.

OPTIONS;
1/425
3/1352
13/425
13/1352

Answer 1

1/425 that 8s the answer

Answer 2

Answer: The correct option is (A)
`(1)/(425).`

Step-by-step explanation: We are given to consider an example of a deck of 52 cards.

We are to find the probability of drawing three queens from a standard deck of cards, given that the first card drawn was a queen and the cards are not replaced.

We know that there are 4 queens in a deck of 52 cards.

Since the first card is already a queen and the cards are not not being replaced, so we have 3 options for 2nd queen and 2 options for 3rd queen.

That is, the total number of options for three queens is given by

`n=3*2=6.`

Now, after drawing first queen, 51 cards left in the deck and after drawing second queen, 50 cards left in the deck.

So, the probability of drawing three queens from a standard deck of cards, given that the first card drawn was a queen is

`P=(n)/(51*50)=(6)/(2550)=(1)/(425).`

Thus, the required probability is
`(1)/(425).`

Option (A) is correct.