How do you apply ratios to probability?

Answer 1

Ratios and probabilityPerhaps this question is best answered with examples right off the bat.

Let's say you have two regular fair dice (six-sided, of course). If you throw them 360 times and keep track of the numbers you throw, you'll record a seven about 60 times. So, you could say that the ratio of all possible numbers (including sevens) to sevens to is 360 to 36 (360:60), which is the same as 6 to 1 (6:1). You could also say that the ratio of all OTHER numbers (excluding sevens) to sevens to is 300:60, or 5:1.

(there is no seven on a six sided die....)

You would have also recorded about 50 occurrences of sixes, so you could say that the ratio of sevens to sixes is 60 to 50, or 6 to 5 (6:5). Obviously, the ratio of sixes to sevens would be 5:6.

How about this:

Let's say that the probability that a certain type of rare snake will have male offspring is 0.4. Obviously, the probability of the snake's having female offspring is 0.6. If the snake has lots of offspring, the ratio of males to females will be 0.4 to 0.6, which is the same as 4 to 6, which is the same as 2 to 3 (2:3). Stated another way, for every five snakes born, two will be male, and three will be female.

By the way, whenever possible, it's a good idea to express ratios as close as you can to whole numbers, like 3:2 or 7:5. Also, whenever one of the digits is a one, it's particularly useful, like 3:1 or 9:1, or even 1.5:1. That last ratio, 1.5:1, is equal to 3:2. It depends on what you're more comfortable with.