1. Introduction to probability (4)
Theorems:

2. Introduction to probability (4)
Example: Two dice are tossed; find the probability of getting an even number on the first die or a total number of 8.
Solution:
A: Getting an even number on the first die.
B: The sum of the options obtained on the two dice 8.

3. Introduction to probability (4)

4. Introduction to probability (4)
Example: If the probability that an automobile machine will serve 3, 4, 5, 6, 7 or 8 or more cars on any given workday are respectively: 0.12, 0.19, 0.28, 0.24, 0.10 and What is the probability that it will be serve at least 5 cars on next day at work.
Solution: Let E be the event that at least 5 cars are served

5. Introduction to probability (4)

6. Conditional Probability
The probability of an event B occurring when it is known that some event A has occurred is called a conditional probability and is denoted by
and it can pronounced as “ The probability of B given A”.

7. Conditional Probability
Example: B is an event of getting a perfect square when a die is tossed the die is constructed so that the even numbers are twice as likely to occur as the odd numbers. Find the probability that B occurs relative to the space A and A is the number greater 3.

8. Conditional Probability
Solution:

9. Conditional Probability
Definition:
By the above definition we can solve the above
question by another way as:

10. Conditional Probability
Example:
Employed
Unemployed
Total
Male
460 40
500
Female
140
260
400
600
300
900
If we select one person from above table and the
event is:
M: a man is chosen.
E: the once chosen is employed

11. Conditional Probability
Solution: We can solve the above problem by two methods as:
Directly from table as:

12. Conditional Probability
2. Or

13. Conditional Probability
Example: The listed table is the number of contaminated wafer:
No. Cont.
Center
Edge
Total
0.3
0.1
0.4 1
0.15
0.05
0.2 2 3
0.06
0.04 4
0.01
5 and more
0.07
0.03
0.72
0.28

14. Conditional Probability
Assume that one wafer is selected at random from this set let A denotes the event that a wafer contains four or more particles and let B denotes the event that a wafer is from a center.
Find:

15. Conditional Probability

16. Conditional Probability