Question

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?

Answer 1

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

Answer 2

1/32600

Answer 3

Sorry Thats not the answer

Answer 4

really?

Answer 5

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

Answer 6

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

Answer 7

the second card being a king would be 1/51

Answer 8

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

Answer 9

how they came up with that answer i do not know

Answer 10

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

Answer 11

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

Answer 12

and then 3/51

Answer 13

and ace will be 4/50

Answer 14

So multiply and its 2/5525

Answer 15

ah you got it...nvm

Answer 16

But Btw do you know Why we are multiplying ?

Answer 17

yes

Answer 18

Um Why ?

Answer 19

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

Answer 20

occur

Answer 21

like if you have 10 books and 2 are school books

Answer 22

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

Answer 23

2/10=1/5

Answer 24

yes But we didnt multiply anything here ?

Answer 25

so say you have taken 1 school book out already

Answer 26

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

Answer 27

well we already know the first one was 2/10

Answer 28

well that leaves 1/.9

Answer 29

so you multiply 2/10 x 1/9

Answer 30

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

Answer 31

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

Answer 32

OH Ohkay
Thanks a lot =)

Answer 33

we are multiplying because these are independent events.

\( P(A\cap B)=P(A) \times P(B) \)

Answer 34

yes

Answer 35

Disclaimer: I know this problem has been solved. I am just practicing here.
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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.