Complementary Probabilities

Question

Suppose the probability of an event is 0.40. What are the odds in favor of this event?

The answer is 2 to 3. Can someone plainly explain the math solution to this?

Answer 1

Hi Sally! I think I can help you with that! I like to think of ratios as parts to a whole. If your probability is 40% (or 0.40), then you can also think of your probability as 4/10, further simplified to 2/5. A fraction of 2/5 leaves 3/5 for the the other side of the ratio, giving you hence the ratio of 2:3!

A good way to think about the ratio is as a bag of five balls and your event is a red ball being grabbed. This ratio would mean that for every two red balls in the bag, there are three blue balls. At its most simplified, that is (2 red balls) + (3 blue blues) for a total of 5 balls. Since there are 2 red balls, that gives a probability of (2 red balls)/(5 total balls)= 40%, or a ratio of 2 to 3 (often written as 2:3).

I hope this helps! I am happy to expand on the answer if it was unclear!

Answer 2

If the probability is 0.40, it can be written as 40/100 = 4/10 = 2/5. That means there are 2 successes for every 5 events.

"Odds in favor of an event" is defined as the number of success divided by the number of failures. There are 2 success for every 5 events so that means 2 successes and 3 failures make up the 5 events. So the "odds in favor" are 2:3