Transcript 9.7 Probability of Multiple Events

11.3 Probability of
Multiple Events
Learning goal
• find the probability of the event A and B
• find the probability of the event A or B
Vocabulary
dependent events : when the
outcome of one event affects the
outcome of a second event
independent events : when the
outcome of one event does not affect
the outcome of the second event
Ex 1
Classify as dependent or independent
• Spin a spinner. Then, select a marble from a bag
that contains marbles of different colors.
• Select a marble from a bag that contains marbles of
two colors. Put the marble aside, and select a
second marble from the bag.
• What if we put the marble back???
Probability of A and B
If A and B are independent events, then
P(A and B) = P(A)●P(B)
Ex 2
A box contains 20 red marbles and 30 blue marbles.
A second box contains 10 white marbles and 47 black
marbles. If you choose one marble from each box
without looking, what is the probability that you get
a blue marble and a black marble?
Vocabulary
mutually exclusive events : when two
events cannot happen at the same time.
If A and B are mutually exclusive events, then
P(A and B) = 0.
Ex 3
Are the events mutually exclusive?
• Rolling an even number and rolling a number
greater than 5 on a number cube?
• Rolling a prime number and a multiple of 6 on a
number cube?
• Rolling an even number and rolling a number less
than 2 on a number cube.
Probability of A or B
• If A & B are mutually exclusive events, then
P(A or B) = P(A) + P(B)
• If A & B are NOT mutually exclusive events,
then
P(A or B) = P(A) + P(B) – P(A and B)
Ex 4
At a restaurant, customers get to choose one of four
vegetables with any main course. About 33% of the
customers choose green beans, and about 28% choose
spinach. What is the probability that a customer will
choose beans or spinach?
Ex 5
A spinner has twenty equal size sections numbered
from 1 to 20. If you spin the spinner, what is the
probability that the number you spin will be a multiple
of 2 or a multiple of 3?
Ex 6
• What is the probability of selecting a
square or a red token?
• What is the probability of selecting a token
that is green or a square?
Ex 7
Find the probability of selecting a boy or a blond
person from 12 girls, 5 of whom have blond hair, and
15 boys, 6 of whom have blond hair.
Ex 8
A bank contains 4 nickels, 4 dimes and 7 quarters.
Three coins are removed in sequence without
replacement. What is the probability of selecting a
nickel, a dime and a quarter in that order?
Ex 9
Given a standard deck of cards, find
P(5 or Jack)
P(king or spade)
P(both red or both queens) if 2 cards are drawn
without replacement
Ex 10
There are 5 male and 5 female students. A
committee of 4 members is to be selected at
random. Find P(all female).