CK-12-Basic Probability and Statistics Concepts - A Full Course

4.5. Geometric Distributions http://www.ck12.org

• ais the number of trials ending in 1 success


• pis the probability of success


• qis the probability of failure

Example A

Consider the coin game where the game ends once someone flips tails. What is the probability that the game ends
on the 3rd flip?

a=3 because there are 3 trials

q=. 5

p=. 5

P(atrials) =q(a−^1 )×p

P(3 trials) =

(

1

2

)( 3 − 1 )

×

1

2

P(3 trials) =

(

1

2

) 2

×

1

2

P(3 trials) =. 125

Example B

Suppose a copy machine consistently has a 5% chance of breaking on any given day. Although it might work for
many days in a row, it will inevitably break down. What is the probability that it lasts a whole five day work week
and breaks down on the 6th day?

Although it is counter-intuitive “success” is defined in this problem to be the machine breaks down.

p=. 05

q=. 95

P(6 trials) =. 955 ×. 05 =. 039

Example C

Consider the coin game again and make a probability distribution for games lasting up to 8 coin flips.

TABLE4.2:

a (number of flips) Probability

1. 50 ×. 5 =. 5

2. 51 ×. 5 =. 25

3. 52 ×. 5 =. 125

4. 53 ×. 5 =. 063