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In a standard deck of cards, what is the probability of drawing a diamond OR a face card? Answer choices are in the form of a percentage, rounded to the nearest whole number.a.)50%b.)25%c.)17%d.)42%

Question

In a standard deck of cards, what is the probability of drawing a diamond OR a face card? Answer choices are in the form of a percentage, rounded to the nearest whole number.a.)50%b.)25%c.)17%d.)42%

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Solution

To solve this problem, we need to understand that a standard deck of cards has 52 cards: 13 cards from each of the four suits (hearts, diamonds, clubs, and spades).

Step 1: Calculate the probability of drawing a diamond. There are 13 diamonds in a deck of 52 cards. So, the probability of drawing a diamond is 13/52 = 0.25 or 25%.

Step 2: Calculate the probability of drawing a face card. There are 12 face cards in a deck (the king, queen, and jack of each suit). So, the probability of drawing a face card is 12/52 = 0.23 or 23%.

Step 3: Calculate the probability of drawing a diamond or a face card. Here, we need to be careful because the diamond face cards have been counted twice - once in the diamond count and once in the face card count. There are 3 diamond face cards. So, we subtract the probability of drawing a diamond face card from the sum of the probabilities calculated in steps 1 and 2.

The probability of drawing a diamond face card is 3/52 = 0.058 or 5.8%.

So, the probability of drawing a diamond or a face card is 25% + 23% - 5.8% = 42.2%.

Rounded to the nearest whole number, the answer is 42%.

So, the correct answer is d.) 42%.

This problem has been solved

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