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:

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

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) =

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.

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) =

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) =

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.

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) =

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) =

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.

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)

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.

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) =

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

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

The rest of the Mixed Practice

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) =

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) =

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) =

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