# Geometric distribution

### Geometric distribution

#### Lessons

$P(n)=(1-p)^{n-1}p$
$n$: number of trials until the first success
$p$: probability of success in each trial
$P(n)$: probability of getting your first success in the $n^{th}$ trial
• Introduction

• What is Geometric Distribution?
• Geometric Formula
• Geometric Calculator Commands

• 1.
Determining the Geometric Distribution
Identify which of the following experiments below are geometric distributions?
i.
Flip a coin until it comes up heads. What is the probability that this will take 5 flips?
ii.
Flip a coin 5 times. What is the probability that you will get 1 head?
iii.
An urn contains 7 red balls and 5 white balls. Balls are drawn out of the urn without replacement until a white ball is drawn, what is the probability that the first white ball will be drawn after the 3rd draw?
iv.
There is a certain floober machine that produces knick-knacks. This machine produces a defective knick-knack with probability 0.1. What is the probability that this machine will produce its first defective knick-knack on the 8th knick knack it produces?

• 2.
There is a certain floober machine that produces knick-knacks. This machine produces a defective knick-knack with probability 0.1. What is the probability that this machine will produce its first defective knick-knack on the 8th knick knack it produces?

• 3.
In the game Dungeons and Dragons a fair 20 sided die (icosahedra) is used. A "critical hit" is when a 20 is rolled.
a)
What is the probability that a critical hit is thrown on the first roll?

b)
What is the probability that it takes less than 3 rolls to roll your first critical hit?

• 4.
Geometric Calculator
Balls are drawn with replacement from an urn containing 9 black balls, and 1 golden ball.
a)
Using your calculator what is the probability that the golden ball is drawn on the 1st draw?

b)
Using your calculator what is the probability that the golden ball is drawn on the 2nd draw?

c)
Using your calculator what is the probability that the golden ball is drawn on the 3rd draw?

d)
Using your calculator what is the probability that the golden ball is first drawn on one of the first 5 draws?