Question 1203505: Jose is at a charity fundraiser and has a chance of receiving a gift. The odds in favor of receiving a gift are 4/19. Find the probability of Jose receiving a gift.
A child has a box of candy which might have a toy inside. The probability of the box having a toy is 13/18. What are the odds against the box having a toy?
Found 2 solutions by greenestamps, math_tutor2020:
Answer by greenestamps(13214)   (Show Source):
You can put this solution on YOUR website!
Basic definitions....
The "odds in favor of" compares number of good outcomes to number of bad outcomes.
The "odds against" compares number of bad outcomes to number of good outcomes.
The probability of an outcome compares the number of good outcomes to the number of all possible outcomes.
Note: Probabilities are nearly always given as fractions (or decimals, or percentages). Odds are usually given as ratios, e.g., A:B. But sometimes, as in your post, they are also given as fractions, which I think is confusing.
Examples...
If the odds in favor of an outcome are 3:16, then the odds against are 16:3 and the probability is 3/(16+3) = 3/19.
If the probability of an outcome is 3/8, then the odds in favor are 3:5 and the odds against are 5:3.
If the odds against an outcome are 20:1, then the odds in favor are 1:20, and the probability is 1/21.
Use those examples to answer your questions.
Answer by math_tutor2020(3817)  (Show Source):
You can put this solution on YOUR website!
Problem 1
The portion The odds in favor of receiving a gift are 4/19 should read The odds in favor of receiving a gift are 4:19
I changed the 4/19 to 4:19
Odds in favor and odds against are usually written as ratios separated by a colon.
This is to distinguish them from a similar (but not identical) concept of probability.
When read out loud, the colon is read as "to". Reading "4:19" out loud would be "4 to 19".
The odds in favor of receiving a gift are 4:19
This means there are 4 instances where Jose will get a gift and 19 instances where he doesn't.
The informal template would be gift : no gift
Odds against has us swap those items to have the template no gift : gift
Jose has 4 ways to get a gift out of 4+19 = 23 outcomes total.
The probability Jose gets a gift is therefore 4/23 which is the final answer to problem 1.
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Problem 2
The probability of the box having a toy is 13/18.
There are 13 instances where the box has a toy out of 18 instances total.
18-13 = 5 of those instances do not have a toy.
The odds against template no toy : toy would update to 5:13 which is the final answer to problem 2.
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