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Using Addition with Probability

Essential Question How do I find the probability of inclusive and mutually exclusive events?

Steps… 1.Determine if the events are inclusive or mutually exclusive. 2.Choose the correct formula Inclusive: p(A or B)=p(A)+p(B) – p(A and B) Exclusive: p(A or B)=p(A) + p(B) 3. Substitute into the formula and simplify to find the probability (leave answers in simplest fractional form).

Inclusive Events Events that can occur at the same time Ex. Rolling a 2 or an even number on one roll of a number cube.

Mutually Exclusive Events Events that cannot occur at the same time Ex. Selecting a red card or an ace of spades from a deck of cards.

Example 1 Rolling a number cube once – label the problem Inclusive or Mutually Exclusive and find the probability of each event: A 1 or 4 is rolled Inclusive or Mutually Exclusive? Mutually Exclusive p(A) + p(B) 1/6 + 1/6 = 2/6 = 1/3

Example 2 Rolling a number cube – label I or ME and find the probability of the event: Rolling a number greater than 2, or a 6. I or ME? Inclusive p(A)+p(B) – p(A and B) 4/6 + 1/6 – 1/6 = 4/6 = 2/3

Open your book to page 656 We are going to do #’s 16 and 20 together.

Assignment: Pg 656 #’s 4-5, 7-27 all (4 and 5 refer to a table on page 654)

Do Now A number cube is rolled once, and the number on the top face is recorded. Label the event I or ME, then find the probability. 1.4 or 5 2.Even # or a 6 3.Odd # or a 2 4.A # less than 3 or a 1

Pg , /25 (64%) 5.59/100 (59%) 7.1/3 8.1/3 9.2/3 10.2/3 11.½ 12.2/3 13.5/6 14.1/ ME, 1/9 17.ME, 1/6 18.ME, ¾ 19.ME, 25/36 20.I, 35/36 21.I, 5/6 22.I, 1 23.I, 1 24.ME, 5/6

Continued… 25.ME, 13/18 26.ME, 1 27.I, 1

(1,1)(1,2)(1,3)(1,4)(1,5)(1,6) (2,1)(2,2)(2,3)(2,4)(2,5)(2,6) (3,1)(3,2)(3,3)(3,4)(3,5)(3,6) (4,1)(4,2)(4,3)(4,4)(4,5)(4,6) (5,1)(5,2)(5,3)(5,4)(5,5)(5,6) (6,1)(6,2)(6,3)(6,4)(6,5)(6,6)

Assignment Pg , 1-14 all Worksheet 10.4, 1-15 all

Pg , #’s 1-14 all 1.ME, 2/13 2.I, 7/13 3.I, 25/26 4.I, 1 5.ME, 1 6.I, 3/13 7.½ 8.½ 9.2/ / / / /5

Worksheet 10.4 #’s I, 4/13 2.ME, 6/13 3.I, 19/26 4.I, 3/4 5.ME, 27/52 6.I, 41/52 7.5/8 8.5/8 9.3/8 10. ¾ / / / / /18

Do Now A card is drawn at random from a standard deck. Tell whether the events are ME or I. Then find the probability. 1.A Jack or a red card 2.A 3 or a 4 3.A face card or an Ace 4.A diamond or not a heart

Assignment A card is randomly drawn from a standard deck. Label ME or I and find the probability. 1.A queen or a heart – 2.A king or a two – 3.A heart or a diamond – 4.A five or a six – 5.A three or a face card –

Assignment continued Using the table on page 656 – label the events ME or I and find the probability. 6.A sum of 3 or a sum of 5 – 7.A sum of less than 4 or sum of greater than 6 – 8.A sum of 10 or a sum of 8 – 9.A sum of greater than 3 or a sum of greater than 7 –

Assignment 10.A product of greater than 5 or a product of less than 8 – 11.A product of less than 15 or a product greater than 10 – 12.A product of less than 6 or a product greater than 12 –

Table 13.A House Dem. or a Senate Repub A House Repub. or a Senate Democrat 15.A Dem or a Senator Find the probability that a randomly selected member of Congress is the following: 16.A Republican or a Senator – DemocratRepublicanTotal House Senate Total