http://www.ck12.org Chapter 4. Probability Distributions
4.5 Geometric Distributions
Here you’ll become familiar with another type of probability distribution called a geometric distribution. You’ll
make connections with a binomial probability distribution and solve for probabilities of events.
Suppose you want to predict how many hands of blackjack it would take to win one hand. You could get lucky
and win on the first hand or you might have to play two, three or even ten hands before you finally win. This is
different from a binomial distribution because a binomial distribution has a limited and finite number of trials while
a geometric distribution has a potentially unlimited number of trials. A binomial distribution also focuses on the
number of successes that occur in n trials while a geometric distribution focuses instead on the number of trials
before the first success.
Watch This
First watch this video to learn about geometric distributions.
MEDIA
Click image to the left for more content.CK-12 Foundation: Chapter4GeometricDistributionsA
Then watch this video to see some examples.
MEDIA
Click image to the left for more content.CK-12 Foundation: Chapter4GeometricDistributionsB
Guidance
The geometric distribution comes directly from our knowledge of the binomial distribution. The geometric distribu-
tion focuses on the number of trials before the first success occurs.
Suppose we play a game where we flip a coin until someone flips a tails and then the game is over. The probability
that the game is over on the first flip is 50% because that is the probability that someone flips tails. After the first
trial, if the game is not over then again the coin has 50% chance of getting a tails on the second flip. This means that
the game has a 50% chance of being over on the first coin flip and a 25% chance of being over on the second coin
flip.
The probability of performingatrials before the first success is the same has havinga−1 consecutive failures and
then having one success.
P(atrials) =q(a−^1 )×p