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
There are total 52 cards.26 cards are red and 26 cards are blackOut of 26 red cards; 13 cards are of diamond and 13 cards are of heartOut of 26 black cards; 13 cards are of spade and 13 cards are of clubsIn spade, clubs, heart and diamond there is one card of ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, King, Queen, Jack
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
!!
