FibonacciChick666 one year ago One card is selected from a standard deck of 52 cards. What is the probability that the card is either a diamond or a face card?

1. Nnesha

there are 13 face cards right :P o,O hmm

2. FibonacciChick666

Looking for others' interpretations here. I thought it should be $$\frac{13}{52}+\frac{9}{52}=24/52=12/26=6/13$$

3. FibonacciChick666

I'm reading the problem wrong somehow(or book has a type-o)

4. FibonacciChick666

Yea, 13 face cards nosh

5. Nnesha

and 13 diamonds lol ??? no idea abt cards :P

6. amistre64

some rules define aces as faces

7. FibonacciChick666

They say the answer is 13/52

8. FibonacciChick666

Made that mistake ( I defined an ace as a face first time around)

9. FibonacciChick666

but this is my second go

10. FibonacciChick666

Shouldn't the probability be greater than just diamonds if we have an or and not an XOR?

11. amistre64

if we remove all the face cards, and the diamonds, that is our ... outcome space?

12. amistre64

10+12 = 22 cards that are favored, out of 52 total

13. amistre64

1thru9 jkq 9+12 = 18 ... out of 52 :)

14. FibonacciChick666

wait, only KQJ are face cards.... I think

15. amistre64

XOR doesnt seem to translate well into english prose

16. amistre64

its 11pm .. and i forgot how to add ... im going to bed :)

17. FibonacciChick666

lol, I am a bit confused by your argument. Let me attempt to understand

18. FibonacciChick666

we should have 30 cards not an option

19. ganeshie8

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20. FibonacciChick666

3 suits, A-10 each

21. FibonacciChick666

I added wrong above My conclusion should be 11/26

22. Nnesha

told you then i deleted the comment i thought this is impossible how fib can got it wrong lol

23. FibonacciChick666

lol I can't add today, clearly

24. FibonacciChick666

but still they are claiming 13/52 is the answer

25. FibonacciChick666

@ganeshie8 Would you say 13/52 is incorrect?

26. FibonacciChick666

I mean I think you proved it, but just want confirmation

27. ganeshie8

A : diamonds B : face cards n(A) = 13 n(B) = 12 n(A $$\cap$$ B) = 3 outcomes in favor = n(A $$\cup$$ B) = n(A) + n(B) - n(A $$\cap$$ B) = 13 + 12 - 3 = 22 total outcomes = 52 so p(A $$\cup$$ B) = 22/52

28. FibonacciChick666

here is their argument: "The prob. that a card is either a diamond or a face card is determined as follows: Let D be the event the card is a diamond. Let F be the event the card is a face card. Then, Pr[D}=13/52 and Pr[F]=12/52. We want to compute the probability of the event DUF Pr[DUF]=Pr[D]+Pr[F]-Pr[D(intersect)F]=13/52+12/52-3/13=13/52

29. FibonacciChick666

Ok, so book is def. wrong and I can't add... Great. Thanks guys!