Question 1193975: A card is picked from a standard deck of cards. Find the odds against and odds in favor of selecting a heart
Answer by math_tutor2020(3817)   (Show Source):
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Answers:
Odds against are 3 to 1
Odds in favor are 1 to 3
This is equivalent to writing:
Odds against are 3:1
Odds in favor are 1:3
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Explanation:
There are 13 hearts and 52-13 = 39 non-hearts.
When writing the odds against getting a heart, we write the ratio 39:13
Simply write the number of ways to get what you dont want (those 39 non-hearts), a colon, then write the number of ways to get what you do want (those 13 hearts). The ratio 39:13 fully reduces to 3:1 when you divide both parts by 13.
The ratio 3:1 is read out as "3 to 1". Meaning you are 3 times more likely to get a non-heart than a heart.
The odds in favor of getting a heart is 1 to 3, equivalent to writing 1:3
We swap each part of the previous ratio to get this current one.
Side note: whenever someone lists the odds of an event, and they say the larger number first, they are most likely referring to the odds against the event happening. This would definitely apply to rare events.
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