# How many times more likely is $B$ to happen than $A$?

The probability of $A$ occurring is $0.05$. The probability of $B$ occurring is $0.20$. How many times more likely is $B$ to occur than $A$?

My immediate intuitive response was $4$, but evidently that can't be correct, as that would be implying that an event with $100\%$ likelihood is $20$ times more likely than $A$. Although this question might sound rather trivial, I'm not sure how to go about finding the answer.

• forgive me if i am wrong but whats the problem of an event P(C)=1 being 20 times more likely than A? – johny Mar 5 '17 at 18:07
• Well, think about it this way: let's say you have an event with a probability of $0.05$. Would it make sense to say that another event, which is 20 times more probably, is completely certain to occur? It's only more likely, not certain. Additionally, what if a certain event is 21 times more likely to occur? Would its probability be $1.05$? That wouldn't make sense, as probabilities can't be above $1$. – Skeleton Bow Mar 5 '17 at 18:10
• You have to exlude the cases where one of the probabilities is 1 or 0. If both probabilities are between 0 and 1 (exclusive) than the interpretation is right. – callculus Mar 5 '17 at 18:12
• @callculus sorry, are you talking to me? – Skeleton Bow Mar 5 '17 at 18:13
• Yes. The OP cannot be addressed by using @. – callculus Mar 5 '17 at 18:16