Asingle card is drawn from a deck of 52 cards, find the following
probabilities:
a. result is a queen
b. result is a queen result is a face card
c. result is a heart
d. result is a heart | result is a red card
e. result is a heart result is a black card
f. result is a heart result is not a diamond

a. 1/13

b. 1/78

c. 1/4

d. 1/12

e. 1/6

f. 1/4

Step-by-step explanation:

First, lets write some basic data

a. result is a queen

Each set has one queen; 1 of spade, 1 of clubs, 1 of heart, 1 of heart

There are total 4 queens

Total number of cards is 52

Probability = Number of favourable outcomes/total number of outcomes

Probability = 4/52

Probability = 1/13

b. result is a queen result is a face card

From my understanding, this question is result is a queen given that result is a face card.

Queen: 4 cards

Face card means King, Queen and Jack

Each set has one King, one Queen and one Jack

There are total 4 sets

Therefore, there are 4 Kings, 4 Queens and 4 Jacks

Face cards: 12-4 (because 4 queens have already been taken out) = 8

Total number of cards: 52-4 (because 4 queens have already been taken out) = 48

Probability (A|B) = P(A) * P(A|B)

P(A) = result is a queen = 4/52 = 1/13

P(A|B) = result is a face card = 8/48 = 1/6

Probability (A|B) = P(A) * P(A|B)

Probability (A|B) = 1/13 * 1/6

Probability (A|B) = 1/78 or 0.01282

c. result is a heart

Out of the 52 cards, there are 26 red cards and out of the 26 red cards, there are 13 cards of heart

Heart = 13 cards

Total number of cards = 52 cards

Probability = Number of favourable outcomes/total number of outcomes

Probability = 13/52

Probability = 1/4

d. result is a heart | result is a red card

Result is a heart = P(A) = 13/52 = 1/4

Result is a red card=26/52 Total number of red cards is 26 but 13 cards (heart) are already taken out so 13 will be subtracted from the numerator and denominator

= 13/39 = 1/3

Result is a heart given that result is a red card P(A|B) = 1/3

Probability (A|B) = P(A) * P(A|B)

Probability (A|B) = 1/4 * 1/3

Probability (A|B) = 1/12

e. result is a heart result is a black card

Result is a heart = P(A) = 13/52 = 1/4

Result is a black card=26/52 Total number of cards is 52 but 13 cards (heart) are already taken out so 13 will be subtracted from the denominator

= 26/39 = 2/3

Result is a heart given that result is a black card P(A|B) = 2/3

Probability (A|B) = P(A) * P(A|B)

Probability (A|B) = 1/4 * 2/3 = 1/6

f. result is a heart result is not a diamond

Result is a heart = P(A) = 13/52 = 1/4

Result is not a diamond = there are 13 diamonds in a deck so cards that are not diamond are 52-13 = 39

Total cards = 52 - 13 (because hearts are already taken out) = 39

= 39/39 = 1

Probability (A|B) = P(A) * P(A|B)

Probability (A|B) = 1/4 * 1 = 1/4

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