Download Sect 12.5 Adding Probabilities

Sect 12.5
Adding Probabilities
Finding probability of multiple events that are mutually exclusive:
Means: Two events ___________ occur at the same time.
Examples:
1) Picking a card that is a two or an ace … in other words, a card can’t be both a two and an ace at
the same time.
2) Choosing a pop that is diet or regular … the pop can’t be diet and regular at the same time.
Try it:
In a standard deck of cards, what is the probability that you draw either a 2 or an ace?
P(2 or ace) =
If two events, A and B, are mutually exclusive, then the probability that either A or B occurs is found by:
P(A or B) = P(A) + P(B).
Try another one …
1) Peyton has a stack of 8 baseball cards, 5 basketball cards, and 6 soccer cards. If she selects a card at
random from the stack, what is the probability that it is a baseball or a soccer card?
2) A die is rolled. Find each probability.
a. P(5 or 6)
b. P(at least a 3)
c. P(less than 4)
Inclusive Events: When two events are not mutually exclusive, they are inclusive.
Examples:
1) Selecting a card from a deck that is either a queen or a diamond … in other words, the card could
be both a queen and a diamond at the same time
2) Selecting a pair of pants that is either striped or made of cotton … the pants could be striped and
made of cotton.
Try it …
1) What is the probability of drawing a queen or a diamond from a standard deck of cards?
If two events, A and B, are inclusive, then the probability that A or B occurs is:
P(A) + P(B) – P(A and B)
2) The enrollment at Southburg High School is 1400. Of the 550 students taking French and 700 taking
algebra, 400 take both French and algebra. What is the probability that a student selected at random
takes French or algebra?
Mixed Practice: Determine whether the event is mutually exclusive or inclusive. Then, determine the
probability of the event.
1) A die is rolled. What is the probability of
3) A card is drawn from a standard deck of
cards. What is the probability of drawing a
rolling a 3 or a 4?
king or a queen?
2) A die is rolled. What is the probability of
rolling at least a 4?
4) A card is drawn from a standard deck of
cards. What is the probability of drawing a
jack or a heart?
Probability Practice: A container contains 7 white marbles and 5 blue marbles. Four marbles are
selected without replacement. Write an expression and evaluate each probability, rounding to the nearest
hundredth.
1. P(4 white)
2. P(4 white or 4 blue)
4. P(3 white then 1 blue)
5. P(3 white and 1 blue, any order)
3. P(no white)