A student wants to know why if the odds in favor of an event are 3:4, the probability of the event occurring is not 3/4 How do you respond?
odds in favour of some event
= probability of that event happening : probability of the event NOT happening
so if the odds of something happening is 3: 4
then the probability of the event happening is 3/7
in general if the odds of something is a : b
then prob of that something = a/(a+b)
Well, dear student, when it comes to odds and probability, they can be a bit like friends who are running in different directions at a carnival. You see, odds are this wacky way of expressing the likelihood of something happening, while probability is a more mathematical way of looking at it.
So, when the odds are 3:4, it means that out of every 7 times this event could happen, it's expected to happen 3 times and not happen 4 times. But probability works on a scale from 0 to 1, where 0 means something is impossible and 1 means it's a sure thing.
To convert those odds to probability, you divide the number of favorable outcomes (in this case, 3) by the total number of possible outcomes (which is 3 + 4 = 7). So, the probability of the event occurring is actually 3/7, which is a little different from 3/4.
Remember, in the world of odds and probability, numbers like to play tricks on us, but don't worry, we can always figure them out with a little laughter and some mathematical hocus-pocus!
The odds in favor of an event, expressed as 3:4, and the probability of the event occurring, expressed as 3/4, are not the same because they represent different concepts.
Odds in favor of an event refer to the ratio of the number of favorable outcomes to the number of unfavorable outcomes. In this case, in a sample space of 7 equally likely outcomes (3 favorable and 4 unfavorable), the odds in favor are 3:4.
Probability, on the other hand, represents the likelihood of an event occurring and is calculated by dividing the number of favorable outcomes by the total number of possible outcomes. In this case, the probability is 3/7 (3 favorable outcomes out of 7 possible outcomes).
To summarize, while the odds in favor of an event and its probability are related, they are distinct concepts and are not represented by the same numerical values.
To explain why the probability of an event occurring is not 3/4 when the odds in favor are 3:4, we first need to understand the difference between odds and probability.
Odds refer to the ratio of the number of favorable outcomes to the number of unfavorable outcomes. In this case, the odds in favor of the event are 3:4, meaning that for every 3 favorable outcomes, there are 4 unfavorable outcomes.
However, probability is calculated by dividing the number of favorable outcomes by the total number of possible outcomes. In this situation, we would need to know the total number of favorable and unfavorable outcomes to determine the probability accurately.
Since the odds do not give us the total number of outcomes, we cannot directly convert the odds ratio to a probability fraction like 3/4. Instead, we would need more information to determine the probability.
If we know the total number of favorable and unfavorable outcomes, we can calculate the probability by dividing the number of favorable outcomes by the total number of outcomes. For example, if there are 7 total outcomes (3 favorable and 4 unfavorable), the probability would be 3/7 or approximately 0.43.
Therefore, it's important to remember that odds and probability are different measurements, and we need more information to accurately determine the probability based on the odds.