Question

In a standard deck of cards there 52 cards of which 26 are black and 26 are red. Additionally, there are 4 suits, hearts, clubs, diamonds and spades, each of which has 13 cards. Two cards are drawn from the deck without replacement. S is the event of drawing a spade from the deck, D is the event of drawing a diamond from the deck. Find P(S and D). Give the answer as a decimal rounded to 4 decimal places.
Answer value

Answer 1

Using probability concepts, it is found that P(S and D) = 0.1275.

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• A probability is the number of desired outcomes divided by the number of desired outcomes.
• In a standard deck, there are 52 cards.
• Of those, 13 are spades, and 13 are diamond.

• The probability of selecting a spade with the first card is 13/52. Then, there is a 13/51 probability of selecting a diamond with the second. The same is valid for diamond then space, which means that the probability is multiplied by 2. Thus, the desired probability is:

$P(S \cap D) = 2 \times \frac{13}{52} \times \frac{13}{51} = \frac{2\times 13 \times 13}{52 \times 51} = 0.1275$

Thus, P(S and D) = 0.1275.

A similar problem is given at brainly.com/question/12873219