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

http://www.ck12.org Chapter 4. Probability Distributions

TABLE4.2:(continued)

a (number of flips) Probability

5. 54 ×. 5 =. 031

6. 55 ×. 5 =. 016

7. 56 ×. 5 =. 008

8. 57 ×. 5 =. 004

Guided Practice

Jordan is a student who hates to be called on in class. His teacher randomly calls on students and Jordan knows that
on any given day he has a 10% chance of being called on. What is the probability that on the first day Jordan is
called on? The 2nd day? The 5th day?

Answer:

Use the geometric distribution formula.

TABLE4.3:

Number of Days Probability

1. 90 ×. 1 =. 1

2. 91 ×. 1 =. 09

5. 94 ×. 1 =. 059

Practice

1. Identify whether or not each situation has probabilities which are geometrically distributed:
   (a) The number of plane flights someone makes before they are in a plane crash.
   (b) The number of times your car will turn on before the battery dies.
   (c) The number of times you win at a slot machine out of 5 plays.
   (d) The number of gold medals a country wins in the Olympics.


2. If the probability of winning a game is .4, then what is the probability of losing 5 games in a row and winning
   on the 6th game?


3. If the probability of rolling a 4 on a fair die is^16 , what is the probability of rolling anything but fours for 10
   rolls and then rolling a 4 on the 11th roll?


4. Suppose there is a game that is played until someone rolls a six, then the game ends. Create a probability
   distribution table for games ending in 8 or fewer rolls.


5. If rain falls randomly with a 20% chance of rain on any given day, what is the probability that we suffer a
   drought for 8 days and then finally it rains on the 9th day?


6. Suppose it rains like it does in question 5. What is the probability that we suffer a drought for 5 days and then
   get rain on any/all of the next 5 days?