SOLUTION: If odds against a person passing a test are 10 to 7, what is the probability that this person will pass the test? 7 to 10? Thank you

Question 307042: If odds against a person passing a test are 10 to 7, what is the probability that this person will pass the test?
7 to 10?
Thank you
Found 3 solutions by Fombitz, rapaljer, jim_thompson5910:
Answer by Fombitz(32388)   (Show Source): You can put this solution on YOUR website!
Odds are written as favorable outcomes to unfavorable outcomes.
Probabilities are written as favorable outcomes over total outcomes.
10 to 7 against passing means that 10 out of 17 times the person will not pass (favorable outcomes out of total outcomes) and 7 out of 17 times the person will pass (unfavorable outcomes out of total outcomes).
So 10:7 odds against passing means 7/17 probability the person will pass.
Answer by rapaljer(4671)   (Show Source): You can put this solution on YOUR website!
NO!! If odds against are 10 to 7, then the unfavorable outcomes are 10 and the favorable outcomes are 7. The total outcomes are 17.

Now, probability is number of favorable outcomes divided by total outcomes.

Probability of passing is 7 favorable divided by 16 total, or .

Dr. Robert J. Rapalje, Retired
Seminole State College of Florida
Altamonte Springs Campus
Answer by jim_thompson5910(35256)   (Show Source): You can put this solution on YOUR website!
With a statement like "odds against" the first number is the number of occurrences of failure while the second is the number of occurrences of success. For example, if a horse has the odds of 3 to 2 against it, then 3 times it will lose while 2 times it will win. This is all out of 5 cases. So this means that the probability of winning is

So in general, if the success of an event has the odds against it of m:n, then the probability of success is

In this case, the odds against passing are 10 to 7, which means that the chances of passing the test is which is about a 41.176% chance.
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