3.3: The Addition RuleObjective: To use the addition rule to calculate probabilities

CHS Statistics

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?

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?

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)

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

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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

Addition Rule Examples:

1. You select a card from a standard deck. Find the probability that the card is a 4 or an ace.

2. You roll a die. Find the probability of rolling a number less than three or rolling an odd number.

Addition Rule Examples (cont.):

3. A die is rolled. Find the probability of rolling a 6 or an odd number.

 

 

4. A card is selected from a standard deck. Find the probability that the card is a face card or a heart.

Probabilities Using TablesA 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.

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) =

Assignment:

pp. 132 – 133

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