Question 1203505
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Problem 1


The portion <font color=blue>The odds in favor of receiving a gift are 4/19</font> should read <font color=blue>The odds in favor of receiving a gift are 4:19</font>


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 <font color=red>gift : no gift</font>


Odds against has us swap those items to have the template <font color=red>no gift : gift</font>


Jose has 4 ways to get a gift out of 4+19 = 23 outcomes total.


The probability Jose gets a gift is therefore <font color=red>4/23</font>  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 <font color=red>no toy : toy</font> would update to <font color=red>5:13</font> which is the final answer to problem 2.
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