1. Microsoft produces a New operating system on a disk. There is 0
Microsoft produces a New operating system on a disk. There is 0.12 probability that it will contain just one bug in the programming. There is a 0.08 probability that there may be two bugs, and 0.04 probability that there are 3+ bugs.
What is the probability that you have a bug free operating system?
What is the probability that you have at most 2 bugs in the system?
If you buy TWO disks what is the probability that both disks have 3+ bugs?
If you buy TWO disks what is the probability that at least ONE has a bug? [Hint: P(At Least One) = 1 –P(None)]
WARM UP
1 – ( ) = 0.76
= 0.96
(.04)(.04) =
No Bugs on TWO disks = (.76)(.76)=.5776
P(At least One)= 1 – =

3. If AP Statistics Review sessions were offered, would you likely attend a:
A Saturday Morning Session 9 am to Noon
B After School Session 4:20 – 6:20
C I Would probably NOT attend either.

4. If you answered “B” (Weekday afternoon 4:20-6:20), which day of the week best fits you schedule.
A Monday
B Tuesday
C Wednesday
D Thursday

10. 1.) Are events A and B Independent, Mutually Exclusive, or Neither ?
EXAMPLE 1: If P(A) = 0.40, P(B) = 0.20, and P(A ∩ B) = 0.80
1.) Are events A and B Independent, Mutually Exclusive, or
Neither ?
If Mutually Exclusive: P(A ∩ B) = 0
If Independent: P(A ∩ B) = P(A) ∙ P(B)

11. a.) If X and Y are Mutually Exclusive Find the Probability of X or Y
EXAMPLE 2: Given that P(X) = and P(Y) = 0.36
P(Z) = 0.15 find:
a.) If X and Y are Mutually Exclusive Find the Probability of X or Y
b.) If X and Y are Mutually Exclusive Find the Probability of X and Y
c.) If X and Y are Independent Find the Probability of X and Y
d.) If Y and Z are Independent and X is M.E. to Y and Z, Find the Probability of X or (Y and NOT Z).
P(X U Y) = = 0.61
P(X ∩ Y) = 0
P(X ∩ Y) = .25 x.36 = 0.09
P(X U (Y ∩ Zc) = x .85 = 0.556

12. Example 3 :
56% of automobiles in TX are SUVs. 85% of SUV are Black, 2% are White, and 13% are other colors.
What is the probability that a randomly chosen automobile will be a SUV that is NOT Black?
What is the probability that a randomly chosen automobile is NOT a SUV OR a SUV and its White?
What is the probability that when randomly choosing two SUVs, at least one of them is black?
P(S ∩ Bc) = .56 x .15 = 0.084
P(SC U (S ∩ W)) =
P(SC U (S ∩ W)) = x .02 =
P(At Least 1 Black) = 1 – P(Neither is Black) =
1 – P(Bc ∩ Bc) = 1 – (.15)(.15) =

14. HW: PAGE 341: 21, 26, 29, 30, 32, 33

17. Monty Hall problem
Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, which always a goat. He then says to you, "Do you switch your choice or stay?” What should you do? Does it matter?

18. Monty Hall problem
Do NOT Switch Switch
Win = 33%
Win = 66%

19. 5. A standard Deck of cards has 52 cards four suits of
(2 – 10, J, Q, K, A). Find the Probability of:
Selecting ONE card and that card being a:
1.) Heart or a Club
2.) Heart or a Five
3.) Face Card or a Spade
4.) Red Card or a Face Card
Selecting TWO cards (With Replacement) and obtaining a:
5.) Heart and then a Face Card
6.) Heart and then a Five
7.) Two Aces
8.) Two Red Cards
Selecting TWO cards (Without Replacement) and obtaining a:
9.) Two Aces
10.) Heart and then a Face Card
1/2
4/13
11/26
8/13
3/52
1/52
1/169
1/4
1/221
11/204

20. Selecting ONE card and that card being a:
1.) Heart or a Club
2.) Heart or a Five
3.) Face Card or a Spade
4.) Red Card or a Face Card
Selecting TWO cards (With Replacement) and obtaining a:
5.) Heart and then a Face Card.
6.) Heart and then a Five
7.) Two Aces
8.) Two Red Cards
Selecting TWO cards (Without Replacement) and obtaining a:
9.) Two Aces
10.) Heart and then a Face Card