What is the probability that a card drawn at random from a pack of 52 cards is either a king or a spade?Question 1Answera.17/52b.13/52c.4/13d.3/13
Question
What is the probability that a card drawn at random from a pack of 52 cards is either a king or a spade?
Question 1
Answer options:
- a. 17/52
- b. 13/52
- c. 4/13
- d. 3/13
Solution
The probability of drawing a king or a spade from a deck of 52 cards can be calculated as follows:
Step 1: Determine the total number of outcomes. In a standard deck, there are 52 cards.
Step 2: Determine the number of favorable outcomes for drawing a king. There are 4 kings in a deck.
Step 3: Determine the number of favorable outcomes for drawing a spade. There are 13 spades in a deck.
Step 4: Add the number of favorable outcomes. However, note that by simply adding, we have counted the king of spades twice (once as a king and once as a spade). So, we subtract one from the total to correct for this. This gives us 4 (kings) + 13 (spades) - 1 (king of spades counted twice) = 16 favorable outcomes.
Step 5: The probability of an event is given by the ratio of the number of favorable outcomes to the total number of outcomes. So, the probability of drawing a king or a spade is 16/52 = 4/13.
So, the correct answer is c. 4/13.
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