Answer:
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 black
- Out of 26 red cards; 13 cards are of diamond and 13 cards are of heart
- Out of 26 black cards; 13 cards are of spade and 13 cards are of clubs
- In spade, clubs, heart and diamond there is one card of ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, King, Queen, Jack
<u>a. result is a queen</u>
<em>Each set has one queen; 1 of spade, 1 of clubs, 1 of heart, 1 of heart</em>
There are total 4 queens
Total number of cards is 52
<em>Probability = Number of favourable outcomes/total number of outcomes</em>
Probability = 4/52
Probability = 1/13
<u>b. result is a queen result is a face card </u>
<em>From my understanding, this question is result is a queen given that result is a face card.</em>
<em>Queen: 4 cards</em>
<em>Face card means King, Queen and Jack</em>
<em>Each set has one King, one Queen and one Jack</em>
<em>There are total 4 sets</em>
<em>Therefore, there are 4 Kings, 4 Queens and 4 Jacks</em>
<em>Face cards: 12-4 (because 4 queens have already been taken out) = 8</em>
<em>Total number of cards: 52-4 (because 4 queens have already been taken out) = 48</em>
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
<u>c. result is a heart</u>
<em>Out of the 52 cards, there are 26 red cards and out of the 26 red cards, there are 13 cards of heart</em>
Heart = 13 cards
Total number of cards = 52 cards
<em>Probability = Number of favourable outcomes/total number of outcomes</em>
Probability = 13/52
Probability = 1/4
<u>d. result is a heart | result is a red card </u>
Result is a heart = P(A) = 13/52 = 1/4
<em>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</em>
= 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
<u>e. result is a heart result is a black card </u>
Result is a heart = P(A) = 13/52 = 1/4
<em>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</em>
<em>= 26/39 = 2/3</em>
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
<u>f. result is a heart result is not a diamond</u>
Result is a heart = P(A) = 13/52 = 1/4
<em>Result is not a diamond = there are 13 diamonds in a deck so cards that are not diamond are 52-13 = 39</em>
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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