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%
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%.
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