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Example 2: A fair, 6-sided die is rolled 8 times. The goal is to roll a 1 or a 2 four times during
the experiment.
SOLUTION:
a) Is this a binomial experiment
b) In how many different ways can this event occur
c) What is the probability of this event
a) A success is classified as rolling a 1 or a 2. A failure is classified as rolling a 3, 4, 5, or 6.
Thus, . There are trials and the probability of a success is always , since
the 8 outcomes are independent. Thus, this is indeed a binomial experiment.
b) It is possible to have a success occur in . / different ways.
c) Let be the number of successes possible. Then * +.
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There is about a 17% chance of getting a 1 or 2 on four out of 8 die rolls.
A question that follows from Example 2: is, what does the distribution look like Let‟s develop
the distribution in tabular form first. To do this, we calculate binomial probabilities for each of
the 9 possible outcomes (anywhere between 0 and 8 successes possible).
Successes Probability
0 0.039
1 0.156
2 0.273
3 0.273
4 0.171
5 0.068
6 0.017
7 0.002
8 0.000
Statistics for Decision-Making in Business © Milos Podmanik Page 153