MATH 166 Spring 2016
2.4
c
Wen
Liu
2.4 Bernoulli Trials
Definition: We refer to experiments in which there are just two outcomes as Bernoulli trials. In
this section we are actually not so much interested in performing an experiment with two outcomes
once, but rather many times. We refer to this as a repeated Bernoulli trial.
We make the following very fundamental assumption.
Fundamental Assumption for Bernoulli Trials: Successive Bernoulli trials are independent of
one another.
Let p be the probability of “success” and q be the probability of “failure”. (Naturally, q = 1 − p.) In
general, to find the probability of exactly k successes in n repeated Bernoulli trials, first notice that
any particular sequence with exactly k successes have exactly, n − k failures. Thus by the product
rule, the probability of any one of these occuring is
pk q n−k
The number of ways of obtaining exactly k successes in n trials is the number of ways of selecting
k objects from a total of n. This is C(n, k). The probability of obtaining exactly k successes in n
trials is then
C(n, k)pk q n−k
Technology Corner:
• To find C(n, k)pk q n−k : press 2ND— VARS , scroll down until the A: binompdf(, press ENTER ,
enter n, a comma, p, another comma, k, and finally the parentheses.
• To find the probability of at most k successes: press 2ND— VARS , scroll down until the
B:binomcdf(, enter n, a comma, p, a comma, and then the maximum number of successes.
Examples:
1. It is estimated that one third of the general population has blood type A+. A sample of seven
people is selected at random.
(a) What is the probability that none of them have blood type A+?
(b) What is the probability that exactly three of them have blood type A+?
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MATH 166 Spring 2016
2.4
c
Wen
Liu
(c) What is the probability that at most three of them have blood type A+?
2. Suppose 20% of the restaurants in a certain part of a town are in violation of the health code.
A health inspector randomly selects 7 of the restaurants for inspection. Find the probability
of the following event: at least two of the restaurants are in violation of the health code.
3. A company finds that one out of five employees will be late to work on a given day. If this
company has 43 employees, find the probabilities that the following number of people will get
to work on time.
(a) Exactly 34 workers or exactly 38 workers.
(b) At least 31 workers but fewer than 38 workers.
(c) More than 29 workers but at most 40 workers.
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