Question 1100711
<br>Oops!<br>
The other tutor, who usually supplies good solutions, I think misread or misinterpreted this question.<br>
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.<br>
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).<br>
So a statement of odds compares the number of favorable and unfavorable outcomes.<br>
Probability compares favorable outcomes to the total number of possible outcomes.<br>
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).<br>
So the answer to the question that is asked is 5/7.