## StArAnGeL 3 years ago Three cards are drawn successively, without replacement from a pack of 52 well shuffled cards. What is the probability that first two cards are kings and the third card drawn is an ace?

1. ChrisV

1/((52)(51)(50))

2. ChrisV

1/32600

3. StArAnGeL

4. ChrisV

really?

5. StArAnGeL

Yeah ! The answer is 2/5525 But i need to know how these kind of problems are solved

6. ChrisV

of well the fact is your chance of the first card being a king is 1/52

7. ChrisV

the second card being a king would be 1/51

8. ChrisV

and the third card being an ace would be 1/50

9. ChrisV

how they came up with that answer i do not know

10. ChrisV

unless they are somehow figuring in that there are 4 of each

11. StArAnGeL

Oh Ok there are 4kings So chance of the first card being a king is 4/52

12. StArAnGeL

and then 3/51

13. StArAnGeL

and ace will be 4/50

14. StArAnGeL

So multiply and its 2/5525

15. gogind

ah you got it...nvm

16. StArAnGeL

But Btw do you know Why we are multiplying ?

17. ChrisV

yes

18. StArAnGeL

Um Why ?

19. ChrisV

well to find the probability of something happening you have to multiply the number of times it could possibly occure then divide it by the total number of possibilities

20. ChrisV

occur

21. ChrisV

like if you have 10 books and 2 are school books

22. ChrisV

whats the probability that the first book you pull out of your bag would be a school book

23. ChrisV

2/10=1/5

24. StArAnGeL

yes But we didnt multiply anything here ?

25. ChrisV

so say you have taken 1 school book out already

26. ChrisV

whats the chance of pulling both school book out of the bag in a row

27. ChrisV

well we already know the first one was 2/10

28. ChrisV

well that leaves 1/.9

29. ChrisV

so you multiply 2/10 x 1/9

30. ChrisV

the probability of pulling them both out in order would be 2/90 or 1/45

31. ChrisV

so out of every 90 times you try it, the probability of succedding is 2 times

32. StArAnGeL

OH Ohkay Thanks a lot =)

33. FoolForMath

we are multiplying because these are independent events. $$P(A\cap B)=P(A) \times P(B)$$

34. ChrisV

yes

35. Directrix

Disclaimer: I know this problem has been solved. I am just practicing here. --------------------------------------------------- 4 kings, want 2 4 aces, want 1 no replacement 52 cards in deck P(K) = 4/52. The 52-count drops to 51 with no replacement. King count drops to 3 P(2ndK) = 3/51. The 51 card count drops to 50. King count drops to 2. Ace count remains at 4. P(Ace) = 4 / 50 Using the Multiplication Principle, the probability of these 3 events happening is (4/52) (3/51) (4/ 50) = 2/5525 . Multiplication Principle states: If an event occurs in m ways and another event occurs independently in n ways, then the two events can occur in m × n ways.