Question

How to solve this?There are three events A,B,C one of which must and only one can happen.The odds are 7 to 3 against A and 6 to 4 against B,find the odds against C

I cant understand what to take as the favourable event and total event.And how to solve this

Answer 1

The odds for C are the same as A, or 7 to 3 against.

Explanation:

Notice that for events A and B, we're looking at 10 events in total for both (7 to 3, 6 to 4).

Also notice that we're talking about the odds against the events happening out of 10 tries. A won't happen 7 out of 10 times (which means it will happen 3 out of 10 times). And for B, it won't happen 6 out of 10 times (which means it will happen 4 out of 10 times).

And so out of 10 times, A happen 3 times and B happens 4 times. That leaves 3 times that C can happen (and, in fact, must happen since one and only one event must occur).

And so the odds for C are the same as A, or 7 to 3 against.