Question

A card is chosen from a standard deck of 52 playing cards. Find the probability of drawing a 4 or a diamond. P(4 or diamond). Answer using a fraction or a decimal rounded to the nearest thousandth.

Answer 1

Explanation:

There are 4 cards with the rank 4 in a deck (one for each suit - hearts, diamonds, clubs, and spades), and there are 13 diamonds in the deck (one for each rank from Ace to King).

However, there is an overlap because one of the cards is the 4 of diamonds. So, you need to subtract one from the total number of cards to avoid double-counting.

P(4 or diamond) = (Number of 4s + Number of diamonds - Number of 4 of diamonds) / Total number of cards

P(4 or diamond) = (4 + 13 - 1) / 52

P(4 or diamond) = 16 / 52

Now, you can simplify this fraction by dividing both the numerator and denominator by their greatest common divisor, which is 4:

P(4 or diamond) = (16 / 4) / (52 / 4)

P(4 or diamond) = 4/13

Answer:

So, the probability of drawing a 4 or a diamond from a standard deck of 52 playing cards is 4/13, which is approximately 0.308 rounded to three decimal places.