STA 3381 Lecture Notes - Lecture 2: Conditional Probability
23 May 2018
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Professor
P(failure) = 1-0.99=0.01
Five boxes 1, 2, 3, 4, 5 success or fail example
Event A is when at least on eof hte individual components fail
P(A’)=P(SSSSS)=(0.9)(0.9)(0.9)(0.9)(0.9)=(0.9)^5=0.59
Thus P(A)=1-0.59=0.41
For any event A, P(A) 1.≤
When events A and B are mutually exclulsive (NO OVERLAP), P(A =P(A)+P(B).)⋃B
For events not mutually exclusive, adding P(A) and P(B) results in doublecouting outcomes in
intersection. Tne next result shows how to correct this:
Need to correct doublecounting by subtracting probability of intersection.
For any two events A and B, P(A =P(A)+P(B)-P(A B)
) ⋃B ⋂
Have to get rid of doublecounted intersection!
If we have a triple union,
Add anything that is of an odd order, subtract anything of an even order.
Four
Add
Determining Probabilities Systematically
● Countably inifite
2.3
N might be too large.
Permutations and combinations
● Group of n distinct individuals/objects
○ How many ways are there to select size k from the group
● Bookstore sells 10 diff laptops but can only 3 can be displayed. In how may ways can the three
be chosen?
● Most of the time, we dont care about the order.
○ Like with the laptop example.
● An ordered subset is called a permutation
(order matters!!). An unordered suset is called a
combination
.
○ K elements from a total of n.
For Combinations: Order doesn’t matter, what matters is which ones you select.
Document Summary
Five boxes 1, 2, 3, 4, 5 success or fail example. Event a is when at least on eof hte individual components fail. When events a and b are mutually exclulsive (no overlap), p(a. For events not mutually exclusive, adding p(a) and p(b) results in doublecouting outcomes in intersection. Tne next result shows how to correct this: Need to correct doublecounting by subtracting probability of intersection. For any two events a and b, p(a (cid:1321) b. Add anything that is of an odd order, subtract anything of an even order. How many ways are there to select size k from the group. Bookstore sells 10 diff laptops but can only 3 can be displayed. Most of the time, we dont care about the order. An ordered subset is called a permutation (order matters!!). K elements from a total of n. For combinations: order doesn"t matter, what matters is which ones you select. College of egr example: permutation since order matters.
