Given that 3 cards are dealt without replacement in a standard deck of 52 cards.

Part A:

There are 4 queens in a standard deck of 52 card, thus the probability that the first card is a queen is given by 4 / 52 = 1 / 13.

Since, the first card is not replaced, thus there are 3 queens remaining and 51 ards remaining in total, thus the probability that the second card is a queen is given by 3 / 51 = 1 / 17

Similarly the probability that the third card is a queen is given by 2 / 50 = 1 / 25.

Therefore, the probability that all three cards are queens is given by

$\frac{1}{13} \times \frac{1}{17} \times \frac{1}{25} = \frac{1}{5525}$

Part B:

Yes the probability of drawing a queen of heart is independent of the probability of drawing a queen of diamonds because they are separate cards and drawing one of the cards does not in any way affect the chance of drawing the other card.

Part C:

Given that the first card is a queen, then there are 3 queens remaining out of 51 cards remaining, thus the number of cards that are not queen is 51 - 3 = 48 cards.

Therefore, if the first card is a queen, the probability that the second card will not be a queen is given by 48 / 51 = 16 / 17

Part D:

Given that the first two card are queens, then there are 2 queens remaining out of 50 cards remaining.

Therefore, if two of the three cards are queens ,the probability that you will be dealt three queens is given by 2 / 50 = 1 / 25 = 0.04

Part E:

Given that the first two card are queens, then there are 2 queens remaining out of 50 cards remaining, thus the number of cards that are not queen is 50 - 2 = 48 cards.

Therefore, if two of the three cards are queens ,the probability that the other card is not a queen is given by 48 / 50 = 24 / 25 = 0.96

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3 years ago