I am having trouble with this very difficult probability question. What is the answer?

Question

A man has thirty standard decks of cards, and fifty dice. He shuffles all the cards into one big pile and pulls out ten cards, then he rolls all of the dice. What is the probability that the numbers on all the dice will add up to 67 AND that he pulls at least two ace of spades from the pile?

cidyah · Accepted Answer

(not sure of my answer)
There are 52x30 = 1560 cards and 30 ace of spades
n=10 (number of cards drawn)

10 cards out of 1560 cards can be drawn in 1560C10 ways.
P( 0 ace of spades) = (30C0)(1530C10)/1560C10 = 0.82304
P( 1 ace of spades) = (30C1)(1530C9) /1560C10 = 0.16234

P(at least 2 ace of spades) = 1- P(0 ace of spades)-P(1 ace of spades) = 1-0.823304-0.16234 =0.014356

P( sum = 67) = 1/128119 
http://www.wolframalpha.com/input/?i=sum+of+67+with+30+dice

P( both) = 0.014356/128119 = 0.000000112052

Steve A · Answer

Two ace of spaces = 30/(52*30) * 29/(52*30 -1)

I am having trouble with this very difficult probability question. What is the answer?

2 個解答