Question: Can you solve this Probability problem? (CARDS)?

( Back )

Answer #1:

a) to get two pairs, 8s &4s we need for example the five cards should be: |8| |8| |4| |4| |x| where x is any card that is not 8 or 4.
probability of getting that 1st card |8| is 4cards out of 52 cards total = 4/52
probability of getting that 2st card |8| is 3cards out of 51 cards total = 3/51
probability of getting that 3rd card |4| is 4cards out of 50 cards total = 4/50
probability of getting that 4th card |4| is 3cards out of 49 cards total = 3/49
probability of getting that 5th card |x| is (48-2-2) => 44cards out of 48 cards total = 44/48
note: when we were choosing the |x| card, we take 48 cards total - 2 (4s that are left in the deck) - 2 (8s that are left in the deck) = 44 choices
multiply them together you get: 4/52 * 3/51 * 4/50 * 3/49 * 44/48
however, there are 5! (5 factorial = 5*4*3*2*1) ways you can arrange these 5 cards so that you can get the two pair poker hand.
so the answer is (4/52 * 3/51 * 4/50 * 3/49 * 44/48)*5! = 132 / 54145 which is about 0.24% chance


b)same idea as part a.
|9| |8| |7| |6| |5|
|9| => 4cards out of 52 cards total = 4/52
|8| => 4cards out of 51 cards total = 4/51
|7| => 4cards out of 50 cards total = 4/50
|6| => 4cards out of 49 cards total = 4/49
|5| => 4cards out of 48 cards total = 4/48
remember that they do not have to be in this order, as long as you get the 5 cards in any order you get a straight poker hand. Therefore remember to multiply by 5!
so answer to part b = (4/52 * 4/51 * 4/50 * 4/49 * 4/48)*5! = 64 / 162435 which is about 0.04%

notice that it is harder to get a straight than a two-pair. Therefore in poker, straight > two-pair





** Powered by Yahoo Answers