Page 155 - Statistics for Dummies

Chapter 8: Random Variables and the Binomial Distribution
To calculate “3 choose 2,” you do the following:
This confirms the three possibilities listed for getting two red lights.
Now suppose the lights operate independently of each other and each one
has a 30% chance of being red. Suppose you want to find the probability dis-
tribution for X. (That is, a list of all possible values of X — 0,1,2,3 — and their
probabilities.)
Before you dive into the calculations, you first check the four conditions (from
the section “Checking binomial conditions step by step”) to see if you have a
binomial situation here. You have n = 3 trials (traffic lights) — check. Each trial
is success (red light) or failure (yellow or green light; in other words, “non-red”
light) — check. The lights operate independently, so you have the independent
trials taken care of, and because each light is red 30% of the time, you know 139
p = 0.30 for each light. So X = number of red traffic lights has a binomial distribu-
tion. To fill in the nitty gritties for the formulas, 1 – p = probability of a non-red
light = 1 – 0.30 = 0.70; and the number of non-red lights is 3 – X.
Using the formula for p(x), you obtain the probabilities for x = 0, 1, 2, and 3
red lights:

;

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; and

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