Question

Two cards are drawn in succession without replacement from a standard deck of 52 cards. What is the probability that the first card is a spade given that the second card is a diamond? (Round your answer to three decimal places.)

Answer 1

I have an idea on how to do this but i think im messsing up somewhere along the process

Answer 2

are you familiar with bayes theorem?

Answer 3

yes.. that is what I am using, but I cant seem to get the right answer. I dont know what I am doing wrong

Answer 4

alright lets see what we can do..
D = 2nd card is diamond
S = 1st card is spade

\[P(S | D) = \frac{ P(D|S)P(S) }{ P(D) }\]

Answer 5

so here i think the P(D | S) = (13/52)(13/52)
and P(S) = 13/52

but im not quite sure on how to get the P(D)

Answer 6

sorry p(D|S) = (13/52)(13/51)

Answer 7

well i used the other form of baye theorem

\[P(S|D) = \frac{ P(D|S)P(S) }{ P(D|S)P(S) + P(D|S')P(S') }\]

where \[P(D|S') = {(\frac{ 52-13 }{ 52 })\frac{ 13 }{ 51 } }\]

and P(S') = 39/52

Answer 8

ya i was using P(D) = (39/52)(13/51) + (13/52)(13/51)

Answer 9

but it came out as a low number which it feels kinda wrong unless its correct lol

Answer 10

what did you get?

Answer 11

i was getting .250 and it was wrong

Answer 12

i got around 10% assuming did the algebra correctly, i did it fast so idk if i made a mistake or not

Answer 13

let me calculate it again

Answer 14

I got 0.1 = 10% its pretty low so it feels kinda wrong lol

Answer 15

it has to be rounded to 3 decimal places... do you know the next 2 numbers?

Answer 16

its just 0.1, so 0.100

Answer 17

no its not right :(

Answer 18

yea thought so i didnt think it was right
but idk what exactly im doing wrong

Answer 19

try 0.255 see if it's right

Answer 20

yes!!! that problem was driving me crazy!

Answer 21

thanks!