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3.3: The Addition Rule

CHS Statistics. 3.3: The Addition Rule. Objective : To use the addition rule to calculate probabilities. Warm-up: Something to Consider….

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3.3: The Addition Rule

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  1. CHS Statistics 3.3: The Addition Rule Objective: To use the addition rule to calculate probabilities

  2. Warm-up: Something to Consider… • Suppose there are 300 students in the 11th grade. Fifty-five students are taking French, 54 are taking German, and 9 are taking both French and German. What is the probability of selecting one of these students and he/she is taking French or German?

  3. Mutually Exclusive • Two events are mutually exclusive if they cannot occur at the same time. • For example, a person being a male or female cannot occur at the same time. These events are mutually exclusive. • However, a person being a male or basketball player can occur at the same time. There can be male basketball players. These event are NOT mutually exclusive. • Can you think of other examples of mutually exclusive events?

  4. Addition Rule • Addition Rule for mutually exclusive (ME) events: • P(A or B) = P(A) + P(B) • Addition Rule for non-mutually exclusive (NME) events: • P(A or B) = P(A) + P(B) – P(A and B)

  5. Examples of ME Vs. NME Events: Decide if the following sets of events are mutually exclusive: • Event A: Roll a 3 on a die • Event B: Roll a 4 on a die • Event A: Randomly select a male student • Event B: Randomly select a basketball player • Event A: Randomly select a blood donor with type O blood. • Event B: Randomly select a female blood donor

  6. Standard Deck of Cards (52 total cards) • 4 Suits (13 Diamonds, 13 Hearts, 13 Spades, 13 Clubs) • 4 of each card (A, K, Q, J, 10, 9, 8, 7, 6, 5, 4, 3, 2) • 2 Colors (26 Black cards, 26 Red cards) • 26 Black: • 13 Spades • 13 Clubs • 26 Red: • 13 Diamonds • 13 Hearts

  7. Addition Rule Examples: • You select a card from a standard deck. Find the probability that the card is a 4 or an ace. • You roll a die. Find the probability of rolling a number less than three or rolling an odd number.

  8. Addition Rule Examples (cont.): • A die is rolled. Find the probability of rolling a 6 or an odd number. • A card is selected from a standard deck. Find the probability that the card is a face card or a heart.

  9. Probabilities Using Tables A blood bank catalogs the types of blood, including positive or negative. • Find the probability that the donor has type O blood. • Find the probability that the donor has type O or type A blood. • Find the probability that the donor has type B blood or is negative. • Find the probability that the donor has type O blood or is positive.

  10. Probabilities Using Tables (cont.) People aboard a ship that sunk: You randomly select a person on the same model of ship and route. Using the table above, what is the predicted probability of: • P(man) = • P(man or a boy) = • P(man or someone who survived) = • P(women or someone who died) =

  11. Assignment: pp. 132 – 133 # 1-4, 11 – 22, 25 – 26, 28

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