Probability Revisited
Abstract: This presentation is organized to build off of earlier basics of probability introduced and
to incorporate various applications for probability in life. This includes introduction and use of
expectation, variance, and Bernoulli random variables. The presentation also introduces the binomial,
geometric, negative binomial, hypergeometric, and poisson distributions.
Formulas:
Binomial:
Geometric:
Negative Binomial:
Hypergeometric:
k
Poisson:
Exercise 1:
An airplane has 100 seats. The airline “overbooks” a flight (sells more tickets than available seats) in
order to maximize their profit. Assume that each ticket holder’s decision to show up for a flight is an
independent Bernoulli trial with a probability of showing up for at the flight of .92. (Corporate
passengers make the independent trials assumption more plausible; families make the independent
trials assumption less plausible.) If the airline profit is $10 for each seat sold and the airline loses $40
(and considerable customer goodwill) for each “bumped” passenger, what is the expected profit if 103
seats are sold?
Exercise 2:
A geological study indicates that an exploratory oil well drilled in a particular region should strike oil with
probability p=.2. Find the probability that the 3rd oil strike comes on the 5th well drilled.