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Three cards are drawn from a deck. What is the probability that all the cards are of each suit (heart - spade - diamond - club).

The cards are selected without repetition.

User Mussa
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1 Answer

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Final answer:

The probability of drawing one card from each suit without replacement from a deck can be calculated. The probability is approximately 0.053.

Step-by-step explanation:

The probability of drawing three cards, one from each suit (heart, spade, diamond, and club), from a deck without replacement can be calculated as follows:

Let's start with the first card drawn. There are 52 cards in a standard deck, and 13 cards in each suit.

So, there is a 13/52 chance of drawing a heart as the first card.

Once the first card is drawn, there are 51 cards remaining in the deck.

The probability of drawing a spade next is 13/51, as there are 13 spades left in the deck.

Similarly, after drawing the first two cards, there are 50 cards remaining, and the probability of drawing a diamond is 13/50.

Finally, after drawing three cards, there are 49 cards remaining, and the probability of drawing a club is 13/49.

To find the probability of all four events occurring, we multiply these individual probabilities together:

P(heart, spade, diamond, club) = (13/52) * (13/51) * (13/50) * (13/49)

After simplifying and calculating this expression, we find that the probability is approximately 0.053:

P(heart, spade, diamond, club) ≈ 0.053

User RoeeK
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