Question

If the probability of a certain event is 48/49, what are the odds against the event happening?

a. 48:1
b. 49:48
c. 1:48
d. 48:49

Answer 1

To find the odds against an event with a given probability, calculate the inverse ratio of the probability of the event not happening to the event happening. The probability of the event not happening is the complement of the event's probability. For a probability of 48/49, the odds against the event are 1:48.

Step-by-step explanation:

The probability of an event happening is given as 48/49. To find the odds against the event, we need to look at the probability of the event not happening, which is 1 minus the probability of the event happening. Since the probability of the event occurring is 48/49, the probability of the event not occurring is simply 1 - (48/49), which gives us 1/49.

The odds in favor of an event are given by the ratio of the probability of the event happening to the probability of it not happening. Conversely, the odds against are the inverse of this. So the odds against the event are 1/49 to 48/49, which simplifies to 1:48.

Therefore, the correct answer is (c) 1:48.

Answer 2

The odds against the event happening are d. 48:49.

Step-by-step explanation:

The probability of an event happening is given by the ratio of the favorable outcomes to the total possible outcomes. In this case, the probability of the event is
`\( (48)/(49) \)`.

The odds against the event happening are found by taking the ratio of the unfavorable outcomes to the favorable outcomes. Since there is only one unfavorable outcome (not the event happening) for every 48 favorable outcomes (event happening), the odds against the event happening are expressed as 48:49.

Therefore, the correct answer is d. 48:49.