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.

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

abidemiokin abidemiokin · Answer 2 · 2021-11-18T11:21:12+01:00

The probability that the card is a King is 1/13

Probability is the likelihood or chance that an event will occur.

Probability = Expected outcome/Total outcome

Given that a card is drawn at random from a pack of 52 playing cards, the total outcome is 52

If the card is a king, the expected outcome is 4

Pr(selecting a king) = 4/52 = 1/13

Hence the probability that the card is a King is 1/13

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