Download 3 Probability of Multiple Events - notes

Probability of Multiple Events
SWBAT:
Find the probability of the event A and B, and the event A or B.
On Your Own.
You and your friend are taking turns rolling a pair of dice. If you roll a sum that is either odd or
a prime number, you score a point. If your friend rolls a sum that is odd and a prime number,
she scores a point. Which score is likely yours? About how many turns has each of you taken?
Explain.
Player 1
Player 2
To find the probability of two events occurring together, you must decide whether one event
occurring affects the other event.
When one event affects the outcome of a second event, they are said to be
____________________ events.
When one event DOES NOT affect the outcome of a second event, they are said to be
____________________ events.
Example 1 Classifying Events
Are the outcomes of each trial dependent or Independent?
a. Roll a die. Spin a spinner.
b. Pick a card from a deck and then pick another card.
You Try.
You reach into your pocket and pull out a coin. You put that coin back into your pocket and
then select another coin. Are these events dependent or independent?
Probability of A AND B
If A and B are independent events, then P(A and B) = P(A) · P(B)
Example 2 Finding the Probability of Independent Events.
At the picnic there are 10 regular sodas and 5 diet sodas in a cooler. There is also a bag
containing 8 bags of fat-free chips and 12 bags of regular chips. If you reach into the cooler
and grab a soda, and reach into the bag and grab some chips, what is the probability that you
get a regular soda AND a regular bag of chips?
You Try.
Using the information in Example 2, what is the probability that you get a diet soda and a
regular bag of chips?
Two events that cannot happen at the same time are called____________________________
___________________________________.
Example 3 Mutually Exclusive Events
You roll a single die. Are the events mutually exclusive? Explain.
a. Rolling a 2 and a 3
b. Rolling an even number and a multiple of 3
c. Rolling an even number and a factor of 9
You Try
You roll a single die. Are the events mutually exclusive? Explain.
1. Rolling an even number and a prime number
2. Rolling an even number and a number less than 2
Probability of A OR B
P(A or B) = P(A) + P(B) – P(A and B)
If A and B are mutually exclusive events, then P(A or B) = P(A) + P(B)
Example 4 Finding Probability of Mutually Exclusive Events
At Sterling High School, a student can take one foreign language each year. About 38% of the
students take Spanish. About 22% of the students take Italian. What is the probability that a
student chosen at random is taking Spanish or Italian?
You Try.
1. About 14% of the students take French at Sterling. What is the probability that a
student chosen at random is taking Spanish, Italian, or French?
2. Without knowing how many students are at Sterling High School, can you determine
which language most students take? Explain.
Example 5 Finding Probability
Suppose you reach onto a dish and select a token at random. On the dish there are 2 orange
circles, 2 red circles, 1 orange circle, 1 red square, 1 orange square, 1 green square, and 1
yellow triangle. What is the probability that the token that you get is round OR green?
You Try. Suppose you randomly select another token from the dish. What is each Probability?
1.
the token is square or red?
2. The token is green or square?