convert 1:5 odds to probability

[Jeffrey Chudy]

convert 1:5 odds to probability

[Anonymous]

Question 121 : If the odds of default are 1:5, what is the probability of default?
(a) 16.67%
(b) 50%
(c) 12%
(d) 20%

Hi,
Can you please explain this answer, not sure if there is a typo here.
The correct answer is choice ‘a’

If odds are 1:H, then p = H/(1 + H) and H = p/(1-p). Therefore the correct answer is Choice ‘a’, equal to 1/(1+5). All other choices are incorrect.

If I follow this formula p = H/(1 + H), I get p= 5/(1+5)

Alternatively, if I have 1:2 chance of winning a bet, it seems like the probability should be 50%. The formula would be 1/(1+2) or 33%.

[Anonymous]

Yup – the answer is correct but very poorly explained – my bad. If odds are 1:5, it means that if there are 6 possible outcomes, then 1 of those 6 would have the event happen, and the other 5 will not.

Odds are the ratio between the probability of the occurence of an event to the probability that the event does not occur.
If odds are H, then p = H/(1 + H) and H = p/(1-p). In this case the odds are 1:5, or 1/5, therefore the correct answer is choice a, equal to (1/5)/(1 + 1/5) = 1/6 = 16.67%.

Thank you for pointing out. For your example, if odds are 1:2, you have only 1 in 3 chances of winning, not 1 in 2. That is the difference between odds and probability.

(In some sports etc, I believe odds are quoted the other way round, ie probability of not happening to probability of happening – but here we stick to the way it is explained in the PRMIA handbook.)

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