SOLUTION: Two cards are drawn in succession without replacement from a standard deck of 52 cards. What is the probability that the first card is a face card (jack, queen, or king) given that

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Question 1118548: Two cards are drawn in succession without replacement from a standard deck of 52 cards. What is the probability that the first card is a face card (jack, queen, or king) given that the second card is an eight? (Round your answer to three decimal places.)
Found 4 solutions by rothauserc, greenestamps, ikleyn, Alan3354:
Answer by rothauserc(4718)   (Show Source): You can put this solution on YOUR website!
let event A be the probability of first drawing a face card = 12/52 = 3/13
:
let B be the probability of second drawing an 8 = 4/51(because the face card was drawn first)
:
Probability (P) (A|B) = P (A intersection B) / P(B)
:
P (A intersection B) means P that both events happen, therefore
:
P (A intersection B) = (3/13) * (4/51) = 12/663 = 4/221
:
P (A|B) = (4/221) / (4/51) = 51/221 is approximately 0.231
:
Answer by greenestamps(13203)   (Show Source): You can put this solution on YOUR website!


The question doesn't really make any sense. The probability that the first card is a face card is not affected by what card is drawn second.

The solution by the other tutor actually shows this; but it is hard to see because of the way he shows his calculations, and by the fact that his final answer in fraction form is not in simplest form.

Let A represent drawing a face card on the first draw and B represent drawing an 8 on the second. Then

P(A) = 12/52 = 3/13
P(B) = 4/51

Then the conditional probability is

P(A|B) = (P(A and B)/P(B)) = (P(A)*P(B))/P(B) = P(A) = 3/13
Answer by ikleyn(52834)   (Show Source): You can put this solution on YOUR website!
.
The answer to this question is obvious: the probability under the question is   = .


The answer to this question is obvious: the probability under the question is   = .


The answer to this question is obvious: the probability under the question is   = .


Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
This is the 2nd time cards are drawn, yet one of them is "given."
Makes no sense.
Think about it.
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