Given that P(A) = 1/4 , what are the odds against A occurring?

I am not sure how to solve this.

If P(A) = 1/4 then P(not A) = 3/4

so odds against A = (3/4) : (1/4) = 3:1

P(certainty)=1

So P(A) + P(~A) = 1
What would be P(~A), i.e. probability of A not happening)?

To find the odds against event A occurring, you need to calculate the probability of the complementary event (not A) and then find the ratio between these two probabilities.

The probability of the complementary event (not A) occurring is calculated as 1 - P(A). In this case, since P(A) = 1/4, the probability of not A occurring is 1 - 1/4 = 3/4.

To find the odds against A occurring, you need to compare the probability of not A occurring to the probability of A occurring. The odds against A are given by the ratio of the probability of not A to the probability of A.

Odds against A = (Probability of not A) / (Probability of A)
Odds against A = (3/4) / (1/4)
Odds against A = (3/4) * (4/1)
Odds against A = 3

Therefore, the odds against A occurring are 3.