1. Pencil, red pen, highlighter, GP notebook, textbook, calculator
U10D7
Have out:
Bellwork:
Answer the following. Similar types of problems where the most missed on the last test.
1. Factor completely across the rationals. a) b) +3 +2 +3
2. Solve for all solutions of x. a) b)
total:

2. Bellwork: 2. Solve for all solutions of x. a) b) +1 +1 total: +1 +1 +1+2
total: +2

3. Part 1: Let’s formalize AND and OR:
_______________ – any event combining _____ or ________ simple events.
compound events 2
more
Consider: are the events ______________ or ______________?
mutually exclusive
mutually inclusive
_______________ (or ______) – events that _________ occur at the same time. That is, events that do not ________.
Mutually Exclusive
disjoint
CANNOT
overlap
Examples:
Drawing a 5 or drawing a King from a standard deck of cards
Rolling a pair of dice to get a sum of 5 or a sum of 7
P(A) + P(B)
Formula: P (A or B) = ______________
Practice: Given a standard deck of cards, find each probability.
1. P (even number card or king) =
2. P (ace or queen) =

4. Mutually Inclusive
________________ – events that can occur at the __________.
same time
Drawing a card that is both a 5 and a heart from a standard deck of cards.
Examples:
Rolling a pair of dice to get a 6 and rolling an even number
Since inclusive events can happen simultaneously, DO NOT ____________ the probability when the events ________.
double count
overlap
Formula: P (A or B) =
P(A) + P(B) – P(A and B)
P (A and B) =
probability that A & B both occur at the same time
subtract
We _______ P (A and B) in the above formula to remove any overlap.

5. Practice: Given a standard deck of cards, find each probability.
1. P(Drawing a red card) =
2. P(Drawing a king) =
3. P(Drawing a red card and king) =
4. P(Drawing a red card or a king) =
P(Drawing a red card) + P(Drawing a king) – P(red and king) =

6. Practice: Given a standard deck of cards, find each probability.
5. P(Drawing a diamond) =
6. P(Drawing a face card) =
7. P(Drawing a diamond and a face card) =
8. P(Drawing a diamond or a face card) =
P(diamond) + P(face card) – P(diamond and face card) =

7. Whatever is not finished must be completed later.
You have 5 minutes to complete the first several problems on the Mixed Practice.
Whatever is not finished must be completed later.

8. Mixed Practice: Complete the area table for the outcomes of the event {roll two dice and find the sum} to find the probabilities.
First Die 1 2 3 4 5 6 7 8 9 10 11 12
Mutually exclusive
P(A or B) = P(A) + P(B)
1. P(sum is 2 or sum is 5) =
Second Die
2. P(sum is a multiple of 2 and sum is a multiple of 5) =
It’s an AND, so we’re good!
Inclusive.
P(A or B) = P(A) + P(B) – P(A and B)
3. P(sum is a multiple of 2 or sum is a multiple of 5) =

9. First Die
4. P(Both die are the same and sum < 8) = 1 2 3 4 5 6 7 8 9 10 11 12
It’s an AND, so we’re good!
Second Die
Inclusive.
P(A or B) = P(A) + P(B) – P(A and B)
5. P(Both die are the same or sum < 8) =

10. Finish the rest of the Mixed Practice later.
First Die
6. P(sum = 7) = 1 2 3 4 5 6 7 8 9 10 11 12
7. P(Odd Sum) =
Second Die
8. P(sum = 7 and Odd Sum) =
9. P(sum = 7 | Odd Sum) =
Finish the rest of the Mixed Practice later.

11. HHH TTT HHT TTH HTH THT HTT THH Part 2: Complementary Events
Recall the sample space for flipping a coin 3 times:
HHH
TTT
HHT
TTH
S =
HTH
THT
HTT
THH
Let A = the event of getting at least 2 heads.
Then P(A)=
How would we describe all the elements of S other than A?
At most one head
(or at least 2 tails)

12. Thanks! You have lovely hair!
We call this AC (that is, A __________), which means everything ____ A.
complement
but
Therefore, P(AC) = ______, so P(AC) + P(A) = __________
Complement: The set of all __________ in the sample space that are ____ included in the outcomes of event A.
Rule: P(AC) = ____________
outcomes
not
1 – P(A)
You have lovely teeth!
Thanks! You have lovely hair!
Okay, maybe we aren’t talking about these kinds of compliments.

13. Practice: Let’s return to the area model for the sum of 2 dice.
Determine the following probabilities for the given events.
1) A = odd sum
P(A) =
AC =
P(AC) =
First Die 1 2 3 4 5 6 7 8 9 10 11 12
Not odd (or just even)
Second Die
2) A = sum > 6
P(A) = AC = P(AC) =

14. Practice: Let’s return to the area model for the sum of 2 dice.
Determine the following probabilities for the given events.
First Die 1 2 3 4 5 6 7 8 9 10 11 12
3) A = both dice are the same #
P(A) =
AC =
P(AC) =
Second Die
Both dice are not the same
4) A = at least one die shows a 3
P(A) = AC = P(AC) =
No threes

15. Finish the worksheets and
PM 85,88, 89, 91

16. The rest of the Mixed Practice

17. 1 2 3 4 5 6 7 8 9 10 11 12 10. P(sum is a multiple of 4) = First Die
Second Die
12. P(sum is a multiple of 3 and sum is a multiple of 4) =
13. P(sum is a multiple of 4 | sum is a multiple of 3) =
14. P(sum is a multiple of 4 or sum is a multiple of 3) =

18. 1 2 3 4 5 6 7 8 9 10 11 12 First Die 15. P(both die are the same) =
Second Die
16. P(Sum > 7) =
17. P(Both die are the same and sum > 7) =
18. P(Both die are the same | sum > 7) =
19. P(Both die are the same or sum > 7) =

19. 1 2 3 4 5 6 7 8 9 10 11 12 First Die 20. P(At least one die is a 4) =
Second Die
21. P(Sum = 9) =
22. P(At least 1 die is a 4 and sum = 9) =
23. P(Sum = 9 | at least 1 die is a 4) =

20. 3/8/13 Have out: Bellwork: Solve for all solutions of x. 1) 2) + 4 + 4
Pencil, red pen, highlighter, GP notebook, textbook, calculator
3/8/13
Have out:
Bellwork:
Solve for all solutions of x. 1) 2)
+2 factor
+1 ZPP +2
+ 4
+ 4 +1 +1 +1 +1 +1 +1
total: +2 +2