This document discusses binomial distributions and provides examples of calculating probabilities of outcomes when sampling from a finite population with a fixed probability of success on each trial. Some examples included are calculating the probability of the number of girls in a family of four children and the probability of getting a certain number of defective tires when sampling randomly from a shipment where a known percentage are defective.

1. Working With Binomial
Distributions
or all about alarm clocks
Puzzle Alarm Clock by evadedave

2. How many girls are there
in a family of four children.
Find the probability of there being
0, 1, 2, 3, or 4 girls in the family.

3. Type of Distributions...
Binomial Distribution: data is discrete (# of heads when ten
coins are tossed, # of spades in a 13 card hand , etc.). When a
binomial experiment is conducted many, many, many times a
portion of the related histogram approaches the shape of the
normal curve.
Probability of the
number of girls in a
family of four.
Experimental Binomial
(Probability)
Theoretical Binomial
Distribution
(Probability)
Distribution

4. Theoretical Binomial
(Probability) Distribution
binompdf(trials, p, x [this is optional])
trials = number of trials
p = P(success)
x = specific outcome

5. The Binomial Coin Experiment
http://www.math.uah.edu/stat/applets/BinomialCoinExperiment.xhtml

6. • When a manufacturer guarantees a toaster for one year, the
toaster will work fine or fail in one year. The manufacturer knows
that, on average, 5 percent of the toasters fail. What is the
probability that the manufacturer will have to replace 120 or more
toasters in a year when 2000 toasters are sold?
binompdf(trials, p, x [this is optional])
trials = number of trials
p = P(success)
x = specific outcome

7. In a 13 card hand, what is the probability of getting exactly 6 spades?
In a 13 card hand, what is the probability of getting 6 or more
spades?

8. There are five children in a family. Assume that boys and girls are
equally likely.
HOMEWORK
1. What is the probability that three are girls?
2. What is the probability that there are at most three girls
(i.e., there may be 0, 1, 2, or 3 girls)?
3. What is the probability that there are more than two girls?

9. A shipment of 200 tires from a tire manufacturing company is
known to include 40 defective tires. Five tires are selected at
random, and each tire is replaced before the next tire is selected.
(a) What is the probability of getting at most 2 defective tires?
HOMEWORK
(b) What is the probability of getting at least 1 defective tire?
(c) What is the probability of getting 2 or 3 defective tires?

10. At a certain hospital, the probability that a newborn is a boy is
0.47. What is the probability that between 45 and 60 (inclusive) of
the next 100 babies will be boys?
HOMEWORK