Answer:
The probability is 0.231
Step-by-step explanation:
In this question, we are tasked with calculating the probability that out of two cards drawn with replacement from a pack of cards , at least one of the two is a face card.
In a standard pack of cards, there are 52 cards.
Now let’s calculate the number of face cards we have.
There are 12 face cards in a pack of cards. There are 4 of each of Jack, Queen or King
The probability of drawing a face card is 12/52 = 3/13
Now, we want to calculate the probability of at least one of the cards drawn are face cards.
Mathematically, what we are needing to calculate is
Probability of drawing a single face card or probability of the two being a face card
Now let’s calculate.
The probability of the first card drawn being a face card is 3/13. The probability of the second card not being a face card will be 1-3/13 = 10/13
The joint probability under this first set of condition will be 3/13 * 10/13 = 30/169
Now, for the second condition, here we are considering that both cards drawn are face cards. What we have is 3/13 * 3/13 = 9/169
Now in probabilities, whenever we are having the statement or, we add the probabilities together
Thus, the probability here would be 30/169 + 9/169 = 39/169 = 3/13
In decimal this will be 0.231
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