Question

The odds in favor of event A are 2 to 1. The odds against event B are 2 to 1. Which event is more likely to occur, event A or event B.

Answer 1

Answer: Event A is more likely to occur.

Explanation:

The odds is the ratio of the number of outcomes support event will occur to the number of outcomes support event will not occur.

Given : For any events A and B , we have

The odds in favor of event A are 2 to 1.

i.e.
`\frac{\text{Event A occur}}{\text{Event A will not occur}}=(2)/(1)`

Probability of having A=
`P(A)=(2)/(1+2)=(2)/(3)`

The odds against event B are 2 to 1.

i.e.
`\frac{\text{Event B will not occur}}{\text{Event B will occur}}=(2)/(1)`

Probability of having B=
`P(B)=(1)/(1+2)=(1)/(3)`

Since ,
`P(A)>P(B)` as
`(2)/(3)>(1)/(3)`

Therefore , the event A is more likely to occur .