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Understanding Probability: Inclusive vs. Mutually Exclusive Events

This guide covers the key concepts of inclusive and mutually exclusive events in probability. It includes step-by-step instructions to determine the type of events and how to calculate their probabilities using the appropriate formulas. Examples such as rolling dice and drawing cards illustrate when events may occur together or not at all. The guide also provides practice problems to reinforce learning, making it an essential resource for mastering probability concepts.

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Understanding Probability: Inclusive vs. Mutually Exclusive Events

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  1. Page 973, 10.3, 1-14 • 10 • 35 • 56 • 9 • 120 • 60 • 1 • 7% • 43% 10. 38% 11. Permutation 12. Permutation 13. Combination 14. Combination, 18%

  2. Using Addition with Probability

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

  4. Steps… • Determine if the events are inclusive or mutually exclusive. • 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).

  5. 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.

  6. 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.

  7. 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

  8. 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

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

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

  11. 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. • 4 or 5 • Even # or a 6 • Odd # or a 2 • A # less than 3 or a 1

  12. Pg. 656 4-5, 7-27 • 16/25 (64%) • 59/100 (59%) • 1/3 • 1/3 • 2/3 • 2/3 • ½ • 2/3 • 5/6 • 1/2 • 1 • ME, 1/9 • ME, 1/6 • ME, ¾ • ME, 25/36 • I, 35/36 • I, 5/6 • I, 1 • I, 1 • ME, 5/6

  13. Continued… • ME, 13/18 • ME, 1 • I, 1

  14. Assignment Pg. 973 10.4, 1-14 all Worksheet 10.4, 1-15 all

  15. Pg. 973 10.4, #’s 1-14 all • ME, 2/13 • I, 7/13 • I, 25/26 • I, 1 • ME, 1 • I, 3/13 • ½ • ½ • 2/3 • 1 • 3/5 • 3/10 • 4/5 • 3/5

  16. Worksheet 10.4 #’s 1-15 • I, 4/13 • ME, 6/13 • I, 19/26 • I, 3/4 • ME, 27/52 • I, 41/52 • 5/8 • 5/8 • 3/8 • ¾ • 19/36 • 13/36 • 5/9 • 11/18 • 5/18

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

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

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

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

  21. Table • A House Dem. or a Senate Repub. - • A House Repub. or a Senate Democrat • A Dem or a Senator Find the probability that a randomly selected member of Congress is the following: • A Republican or a Senator –

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