Compound Probabilities and Odds 
 Sections 8.8,8.9  
Roll two dice at once.

(1,1)  (1,2)  (1,3)  (1,4)  (1,5)  (1,6)  
(2,1)  (2,2)  (2,3)  (2,4)  (2,5)  (2,6)  
(3,1)  (3,2)  (3,3)  (3,4)  (3,5)  (3,6)  
(4,1)  (4,2)  (4,3)  (4,4)  (4,5)  (4,6)  
(5,1)  (5,2)  (5,3)  (5,4)  (5,5)  (5,6)  
(6,1)  (6,2)  (6,3)  (6,4)  (6,5)  (6,6)  
An experiment consists of throwing two dice, one red and one green. The reason for using 2 different color dice is to emphasize that (1,2) and (2,1) are 2 different throws. 
Solve 
Step 
Find the probability of throwing a sum of 10.  
You can roll (4,6) , (5,5), or (6,4) 
3 ways to roll a 10. 

6 × 6 = 36 different throws. 
Find the probability of throwing a sum of 2 or 4. 

You can roll (1,1) , (1,3), (2,2) or (3,1) 
1 way to roll a 2 and 3 ways to roll a 4 

4 ways total, È means 'or' 

Roll
two dice at once.

[Solution] 


Suppose we pick 2 balls out of a box without replacement. Let's say 5 are red and 7 are blue. What is the probability of picking a red ball then a blue ball? 
Solve 
Step 
Pick red first. Pr(red) = 5/12 
There are a total of 12 balls in the box. 
Then pick blue. Pr(blue) = 7/11 
Notice it is not 7/12 since once we picked a red ball there is one less ball in the box. 
Pr(red then blue) = 5/12 × 7/11 = 35/121 
These events are not independent. 

Suppose we pick 2 balls out of a box without replacement. Let's say 3 are red and 5 are blue. What is the probability of picking a red ball then a blue ball? 
[Solution] 


Suppose we pick 2 balls out of a box with replacement. Let's say 5 are red and 7 are blue. What is the probability of picking a red ball then a blue ball? 
Solve 
Step 
Pick red first. Pr(red) = 5/12 
There are a total of 12 balls in the box. 
Then pick blue. Pr(blue) = 7/12 
The number of balls is not reduced because the question said with replacement. The first ball is put back in the box. 
Pr(red then blue) = 5/12 × 7/12 = 35/144 
These events are independent. 

Suppose we pick 2 balls out of a box with replacement. Let's say 8 are red and 4 are blue. What is the probability of picking a red ball then a blue ball? 
[Solution] 


The odds of winning a race is 3 to 2. Find the probability of winning. 
If the odds in favor of an event are a to b, the probability of the event is 

Solve 
Step 

a = 3 and b = 2 

The probability of winning is 60%. 


The probability of winning a race is 0.70. Find the odds in favor of winning. 
[Solution] 


Tutorials and Applets by
Joe McDonald
Community College of Southern Nevada