Here is the problem: In a game played with a standard deck of cards, each face card has a value of 10 points, each ace has a value of 1 point, and each number card has a value equal to its number. Two cards are drawn at random.
One card is the queen of diamonds. What is the probability that the sum of the cards is greater than 18?
The book says the answer is 19/51, however I got a different answer. Can someone please help me?:
HOW I GOT MY ANSWER:
Probability of (A given B) = P(Sum of two cards is greater than 18 given one is a queen of diamonds) = P(sum of 2 cards is greater than 18 and one of them is a queen of diamonds)/P(drawing a queen of diamonds)
P(drawing a queen of diamonds) = 1/52
P(sum of 2 cards is greater than 18 and one of them is a queen of diamonds) = (1/52)*(15/51) = 5/884
To get a sum greater than 18, I can draw any of the other face cards (11 other) or any card of 9 (4 of those), to get 15/51.
So to get my answer, I evaluated (5/884)/(1/52), to get 5/17, which is clearly not equal to the book answer, 19/51. If there is anything I have done wrong or missed, please tell me, thank you so much!
Also, if there is anything I need to be more clear on, don't be afraid to ask!