SOLUTION: Ifthe odds against an event are 2:5, then the probability of the event = _____

SOLUTION: Ifthe odds against an event are 2:5, then the probability of the event = ______(write answer as a fraction).

Question 1100711: Ifthe odds against an event are 2:5, then the probability of the event = ______(write answer as a fraction).
Found 2 solutions by richwmiller, greenestamps:
Answer by richwmiller(17219) (Show Source): You can put this solution on YOUR website!
3/5
total must equal 1
1-2/5=3/5
Answer by greenestamps(13215) (Show Source): You can put this solution on YOUR website!

Oops!

The other tutor, who usually supplies good solutions, I think misread or misinterpreted this question.

If the odds AGAINST an event are 2:5, then the event will NOT occur 2 times for every 5 times that it DOES occur.

You could equally well say that the odds IN FAVOR OF (or, informally, just "the odds of") the event are 5:2 (that is, it will occur 5 times for every 2 times that it does not occur).

So a statement of odds compares the number of favorable and unfavorable outcomes.

Probability compares favorable outcomes to the total number of possible outcomes.

So odds of 2:5 against an event, or odds of 5:2 in favor of an event, are both equivalent to a probability of 5/7 that the event will occur (or a probability of 2/7 that the event will not occur).

So the answer to the question that is asked is 5/7.
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