Objective To add probabilities to find the probability of either of two mutually exclusive occurring. Why? To know how probability works. As long as it is possible that two events could happen at the same time, the events are not mutually exclusive. (Not M.E. = Cap’t hockey team and member of math club) (M.E. = getting a Jack and a number card in a deck of cards. It c an’t happen.)
California State Standards SDP 3.4: Understand that the probability of either of two disjoint events occurring is the sum of the two individual probabilities… NS 2.1: Solve problems involving addition … of positive fractions … SDP 3.3 : Represent probabilities as ratios, … and percentages between 0 and 100 and verify that the probabilities computed are reasonable; know that if P is the probability of an event, 1 – P is the probability of an event not occurring. MR 3.3: Develop generalizations of the results obtained and the strategies used and apply them in new problem situations.
Vocabulary Mutually exclusive events – Two events that cannot happen at the same time. If one can happen, the other can’t happen An event mutually exclusive to tossing an even number – Tossing an odd number – Tossing a 3 – Tossing a 1 An event not mutually exclusive – Tossing an odd number and tossing a 5 – Tossing a 2 and tossing a number less than 3 – Tossing a number greater than 2 and tossing a number less than 6 Mutually = equally or commonly Exclusive = limited or restricted
How to Add Probabilities 1) Read the problem. Decide if mutually exclusive or not mutually exclusive events. 2) Add the probabilities. Remember ‘or’ means + events. Don’t double count events. 3) Change to a decimal and/or percent. Check your work. Use a cube # 1-6 P(tossing an even # or tossing a 5) Events are mutually exclusive because if one does not happen, the other could not. Even # = 3/6 Toss a 5 = 1/6 3 + 1 = 4 = 2 ≈ 0.667 ≈66.7% 6 6 6 3
How to Add Probabilities 8 spaced spinner (equally spaced) labeled: shirt, belt, doll, ball, glove, daisy, fish, horse. P(article of clothing or 5-letter word). Not mutually exclusive because it could happen. Remember ‘or’ means + events. Clothing and 5-letter words. Don’t double count clothing and 5-letter words. 3/8 + 2/8 = 5/8 5/8 = 0.625 = 62.5%
Try It! 1) and 2) A cube # 1-6. Tell whether events are mutually exclusive or not. Find P as fraction, decimal, percent. Round to nearest whole % 1)P(odd or less than 5) 2)P(4 or prime number) 3)1 student plays basketball and plays the saxophone. M.E.? 1)P(odd or less than 5) Not mutually exclusive because it could happen. P(odd) = 3/6 P(less than 5) = 2/6 3/6 + 2/6 = 5/6 ≈ 0.833 ≈ 83% 2)P(4 or prime number) Mutually exclusive because it could not happen P(4) = 1/6 P(prime number) = 3/6 1/6 + 3/6 = 4/6 = 2/3 ≈ 0.667 ≈ 67% 3) Not Mutually exclusive because it could happen. A student could be both.
Objective Review To add probabilities to find the probability of either of two mutually exclusive occurring. Why? You now know, better, how probability works. As long as it is possible that two events could happen at the same time, the events are not mutually exclusive. (Not M.E. = Cap’t hockey team and member of math club) (M.E. = getting a Jack and a number card in a deck of cards. It c an’t happen.) To find the probability of event A or event B occurring, you can add their probabilities, if the events are mutually exclusive.
Independent Practice Complete problems 4-8 Copy original problem first. Show all work! If time, complete Mixed Review: 9-12 If still more time, work on Accelerated Math.