Binomial Distributions

Calculating Probabilities

The Problem

Let X be a random variable following a Binomial distribution. All Binomial distributions have two parameters: number of trials and success probability. For X, n = 11 and p = 0.77. An example of where such a distribution may arise is the following:

You have a bag of candy made by Statistics, Inc. The company makes only two flavors: sour apple and anchovie. In its processing plant, 77% of the candy made is sour apple. Your bag holds 11 pieces. Define the random variable X as the number of sour apple pieces of candy in your bag.

For those who like pictures, here is a graphic of the probability mass function. Note that the distribution is skewed left:

0.05 0.10 0.15 0.20 0.25 0.30 0 1 2 3 4 5 6 7 8 9 10 11

Continuing the candy example, let us determine the probability that there are exactly 3 pieces of sour apple candy in the bag. In symbols, calculate P[X = 3].

Your Answer

In the box below, please enter the value of P[X = 3], where X ~ Binom(n=11, p=0.77), then click on the “Check your answer!” button. Please round your answer to the ten-thousandths place.

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© Ole J. Forsberg, Ph.D. 2024. All rights reserved.   .