Math

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I was wondering if someone could help me check my work on this problem and see if I'm correct.

Consider the experiment of drawing two cards without replacement from an ordinary deck of 52 playing cards.
What are the odds in favor of drawing a spade and a heart?
There are 52 playing cards in a deck
There are 13 spades and 13 hearts in deck
13 + 13 = 26
P(spade and heart) = 26/52

P(not a spade or heart) = 26/52

Odds in favor of A = Number of ways that A could occur/Number of ways that A could not occur

Odds in favor of A = 26/52 / 1- 26/52 = 0

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Or would it be

Odds in favor of A = 26/52 / 1 - 26/52 = 26 / 51

• Math -

"Odds in favor of A = 26/52 / (1- 26/52)= 0"
A in the above expression actually evaluates to 26/52 / (1-26/52) = (1/2) / (1/2) =1:1

However, I would reason it this way:
The first card can be either a spade or a heart, so the probability is 26/52.
The second card has to the complementary suit, namely a spade if the first one was a heart, and vice versa.
Probability of the second card is therefore limited to one suit out of 51 cards, or 13/51.
Probability of both events happening is
(26/52)*(13/51)=(1/2)*(13/51) = 13/102
Odds are

(13/102) / (1-13/102)
= 13/89
13:89

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I have a question about the answer, how did you get 13/89, I don't understand how you got 89

• Math -

Here it is, in a little more detail:

(13/102) / (1-13/102)
= (13/102) / ((102-13)/102)
=(13/102) / (89/102)
=13/89
=13:89

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