Question

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.

Answer 1

Answer:

The probability of drawing three queens is 1/425

Step-by-step explanation:

* lets talk about the deck cards

- The deck cards has 52 cards

- It has four symbols (heart , diamond , clubs , spades)

- Each symbol has 16 cards (from 1 to 10 and king , queen , princess)

* Lets solve the problem

- We will drawing three cards

- The cards are not replaced

- That means the total of the card will reduce by 1 after each drawing

- The cards will drawing are queens

- The first card drawn will be a queen

∵ The first card drawn is queen

∴ The number of cards for the second drawn is 52 - 1 = 51

∵ There are 4 queens in the deck cards we took one for the first choice

∴ The number of queen for the second choice is 4 - 1 = 3

∴ The probability of second choice is 3/51

- Now there are 2 queens and 50 cards after the second choice

∴ The number of the queen is 3 - 1 = 2

∴ The number of the deck cards is 51 - 1 = 50

∴ The probability of third choice is 2/50

- The probability of the three cards is the product of the two fractions

∴ The probability of drawing three queens = 3/51 × 2/50 = 6/2550

- Simplify the fraction

* The probability of drawing three queens = 1/425

Answer 2

Answer:

The probability of drawing three queens from a standard deck of cards is 0.000162 approximately.

Step-by-step explanation:

Total cards in a deck = 54

No. of queens in a deck = 4

Probability of drawing a queen card = 4/54

Now that 1 queen has been takes, the no. of cards become = 53 and no. of queens = 3

Probability of getting a queen again = (3/53)(4/54)

Probability of drawing three queens in a row without replacement:

Two queens have already been removed. Considering this, we know that:

No. of cards in the deck = 52

No. of queens in the deck = 2

Probability of drawing three queens = (Probability of getting a 3rd queen)x(Probability that the first two from a deck were queen cards)

= (2/52)(3/53)(4/54)

= 0.000162 approximately