Download events

CHS Statistics
Chapter 15A: The Addition Rule
Objective: To use the addition rule to
calculate probabilities
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
•
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 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.
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:
p. 361 # 1 – 3
- Check your answers online.