Question

A card is drawn at random from a pack of 52 playing cards. Given that the card is a diamond, find the probability that the card is a King. Give your answer as a fraction in its simplest form.

Answer 1

Answer:

1/52

Step-by-step explanation:

There is only one of each type of card in each suit.

P(card is a diamond) = 13/52

P(card is a diamond + king) = (13/52)×(1/13) = (13/676) = (1/52)

Answer 2

Answer:  1/13

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Explanation:

Focus only on the diamond cards. There are 13 of them total. Out of the 13 diamond cards, there is one king of diamonds. So the probability of getting a king, if we know 100% the card is a diamond, is 1/13.

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You can use a slightly longer method through a conditional probability

A = card is a king

B = card is a diamond

P(A and B) = probability of king and diamonds = 1/52

P(A \ B) = probability of event A happens given we know B happens

P(A \ B) = P(A and B)/P(B)

P(A \ B) = (1/52)/(13/52)

P(A \ B) = (1/52) ÷ (13/52)

P(A \ B) = (1/52) * (52/13)

P(A \ B) = 1/13