Question

A card is drawn at random from a deck of cards. What is the probability that

(a) it is a heart, given that it is red?

(b) it is higher than a 10, given that it is a heart? (Interpret J, Q, K, A as 11, 12, 13, 14.)

(c) it is a jack, given that it is red?

Answer 1

(A) We know that there are 13 cards of each type, i.e. heart, spade, diamond and club. There are 26 black and 26 red cards in a deck

So, we have 13 hearts and 26 red cards

Probability of heart = Possible outcome/total = 13/52

and probability of red card = Possible outcome/total = 26/52

So, the probability of a heart, given that it is red = (13/52)/(26/52) = 0.5 or 1/2

(B) There are 13 heart cards and 11,12,13 and 14 are greater than 10, i.e. 4 cards greater than 10

So, probability of getting higher than a 10 = Possible outcome/total = 4/52

And probability of hear = Possible outcome/total =13/52

So, probability that it is higher than 10, given that it is a heart = (4/52)/(13/52) = 4/13

(C) There are only two jack of one color, So there will be two jacks of red color

Probability of getting jack = Possible outcome/total = 2/52

and probability of getting red = Possible outcome/total = 26/52

So, the probability of getting jack, given that it is red = (2/52)/(26/52) = 2/26 = 1/13