Question

If odds against an event are 5:8, what is the probability of happening of work?
A.$\dfrac{8}{13}$
B.$\dfrac{5}{13}$
C.$\dfrac{5}{8}$
D.$\dfrac{8}{5}$

Answer 1

Hint: It is given that odds which are against an event are 5:8. It is the ratio of unfavorable outcomes of an event to the favorable outcomes of an event. As it is in the ratio so we have to remove the ratio by multiplying the ratio with x so the number of unfavorable outcomes is 5x and the favorable outcomes are 8x and hence the total outcomes are 13x. We are asked to find the probability of happening of the work which is the ratio of favorable outcomes to the total outcomes so substitute these values that we have found above and you will get the required probability.

Complete step-by-step answer:
It is given that odds against an event are 5:8 which means it is the ratio of unfavorable outcomes of an event to the favorable outcomes of an event.
Odds against of an event $=\dfrac{5}{8}$
Odds against of an event $=\dfrac{\text{Unfavorable outcomes}}{\text{Favorable outcomes}}$
We are asked to find the probability of happening of a work which is the ratio of favorable outcomes of an event to the total outcomes of an event.
To find the favorable and total outcomes we need to convert the ratio into numbers for which we are going to multiply the ratio by “x”.
Unfavorable outcomes of an event = 5x
Favorable outcomes of an event = 8x
Total outcomes of an event = 13x
From the above, we can write the probability of happening of a work as:
Probability of happening of work $=\dfrac{\text{Favorable outcomes}}{\text{Total outcomes}}$
Substituting the values of favorable outcomes and total outcomes from the above in the above equation we get,
Probability of happening of work $=\dfrac{8x}{\text{13x}}=\dfrac{8}{13}$
From the above, the probability of happening at work is equal to $\dfrac{8}{13}$.
Hence, the correct option is (a).

Note: There might be confusion regarding the language of the question “odds against an event are 5:8”. You might misunderstand this statement which is in inverted commas as it is the ratio of unfavorable outcomes of an event to the total outcomes of an event and chose option (c), but actually, it means that it is the ratio of unfavorable outcomes to the favorable outcomes of an event.