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.

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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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.

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

step-by-step explanation:

you divide the denominator by the numerator on both sides and if the quotients are equal then the fractions are equivalent

step-by-step explanation:

there is a formula i can give you:

it is r^2*n*sin(360/n) divided by 2 where r represents the "radius" and n is the number of sides.

plug them in:

(10sqrt(3))^2*6*sin(360/6) divided by 2

100*3*6*sin(60) divided by 2

900*sin(60)

900*sqrt(3)/2

450*sqrt(3)

approx is 779.4 cm^2