Probability?

Question

52 playing cards. They give me 3 cards. What is the probability for me to obtain the 6 and the 7 of hearts? The other card I obtain doesn't matter, it can be whatever card. I've thought of the problem, but couldn't solve it. Please explain your calculous... and thank you SO much! Is it 2/52+2/52+2/52? I guess no, but close.

Answer 1

you meant both 6 and 7 are hearts?
Assume there is no replacement

there is only one 6 that is heart and one 7 that is heart

the probablity of getting the 6 of hearts is 1/52.
After the 6 of hearts is picked out, there are 51 cards left, out of which, only one of them is the 7 of hearts. So the probability that the second card is the 7 of hearts is 1/51.

since the third card doesn't matter, it can be any card, so the probability of getting any card out of 50 remaining cards is 50/50

P = (1/52) (1/51) (50/50)


(1/52) (1/51) (50/50) is the probablity of getting the 6 of hearts first, 7 of hearts second, and a certain card third. But in this problem, but, order does not matter.

since the 3 cards are different from each other, you have 3! = 6 ways to pick the 3 cards

so P = 6 * (1/52) (1/51) (50/50)
P = 1/442 <== answer

Answer 2

a) The total number of admissible choices is (3 choose 2) x 2 x 50=(3!/(2!x1!))x2x50=3x2x50=300.

The reason is that first you have to choose which cards are going to be the 6 and 7 hearts (the 1st and the 2nd you draw, the 1st and the 3rd or the 2nd and the 3rd?) There are (3 choose 2) ways to do this, namely 3 ways. Second, there are two possibilities: either you draw 6 first or 7 first. So 3x2. Finally, there are 50 remaining cards to choose from in order to fill in the 3rd spot as well. So total number=3x2x50=300.

b) The second thing you have to determine is in how many ways you can choose 3 cards out of 52 (without any requirements). There are 52x51x50 ways to do this, because for the first card there are 52 possibilities, for the second only 51 (since you have already chosen one) and for the 3rd one 50.

Probability=(admissible choices)/(total number of choices)=300/(52x51x50).

Answer 3

Hello,

We have the 6 and 7 of hearts so there are 50 other cards left. Then we have 50c1/52c3 which is (50!/49!)/(52!/[49!*3!]) or 50!*3!/52! the we have 50!*3!/(52*51*50!) = 3!/(52*51) or 6/(52*51) = 1/442.

Hope This Helps!!