13.1: Intuitive Illustrations

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Taking a Jellybean from a Bag

Suppose we have an opaque bag of twenty red and green jellybeans. Suppose that there are eight red jellybeans and twelve green ones in the bag.

Red: 8

Green: 12

You mix the jellybeans thoroughly, reach in and, without looking, draw one jellybean from the bag. What is the probability that you draw a red one? There are twenty jellybeans, eight of which are red. So, there are eight ways of getting a red jellybean out of twenty possible cases. We can express this as a fraction, 8/20 (which reduces to 2/5). We will say that the probability of drawing a red jellybean is 2/5.

What is the probability of drawing a green jellybean? Since there are twelve green out of the twenty, there are twelve chances in twenty. So, the probability of drawing a green jellybean is 12/20, which reduces to 3/5.

What is the probability that you will draw either a red jellybean or a green one? Since all the jellybeans are either red or green, you are certain to pick one color or the other. The probability is 20/20, which reduces to 1. What is the probability that you will draw a jellybean that is neither red nor green? None of the jellybeans satisfy this description. Put another way, 0 out of 20 satisfy it. So, the probability is 0/20 which is just 0.

Rolling Dice

You are rolling a fair die (one that isn’t loaded). What are the chances that you will roll a 3? A die has six sides, marked with the numbers 1, 2, 3, 4, 5, and 6. So there is one chance out of six of getting a 3. We say that the probability of rolling a 3 is 1/6.

What are the chances or rolling an even number? There are three ways to roll an even number: rolling a 2, 4, or 6. So the probability is 3/6 (which reduces to 1/2).