Transcript 10.7 Independent-Dependent Events

Objective
Find the probability of independent
and dependent events.
Find the theoretical probability of each
outcome
1. rolling a 6 on a number cube
2. rolling an odd number on a number cube
3. flipping two coins and both landing head up
Adam’s teacher gives the class two list of titles and
asks each student to choose two of them to read.
Adam can choose one title from each list or two
titles from the same list.
Important Vocab
Events are independent events if the
occurrence of one event does not affect the
probability of the other.
Events are dependent events if the
occurrence of one event does affect the
probability of the other.
Example 1: Classifying Events as Independent or
Dependent
Tell whether each set of events is independent
or dependent. Explain you answer.
A. You select a card from a standard deck of
cards and hold it. A friend selects another
card from the same deck.
Dependent; your friend cannot pick the card you
picked and has fewer cards to choose from.
B. You flip a coin and it lands heads up. You flip
the same coin and it lands heads up again.
Independent; the result of the first toss does not
affect the sample space for the second toss.
Example 2: Finding the Probability of Independent
Events
An experiment consists of randomly selecting a
marble from a bag, replacing it, and then
selecting another marble. The bag contains 3
red marbles and 12 green marbles. What is the
probability of selecting a red marble and then a
green marble?
Because the first marble is replaced after it is
selected, the sample space for each selection is the
same. The events are independent.
Example 2 Continued
P(red, green) = P(red)  P(green)
The probability of selecting red
is
, and the probability of
selecting green is
.
Example 3: Finding the Probability of Independent
Events
A coin is flipped 4 times. What is the
probability of flipping 4 heads in a row.
Because each flip of the coin has an equal
probability of landing heads up, or a tails, the
sample space for each flip is the same. The events
are independent.
P(h, h, h, h) = P(h) • P(h) • P(h) • P(h)
The probability of landing
heads up is with
each event.
Suppose an experiment involves drawing marbles
from a bag. Determine the theoretical probability of
drawing a red marble and then drawing a second
red marble without replacing the first one.
Probability of drawing a red marble on the first draw
Suppose an experiment involves drawing marbles
from a bag. Determine the theoretical probability of
drawing a red marble and then drawing a second
red marble without replacing the first one.
Probability of drawing a red marble on the second
draw
To determine the probability of two dependent
events, multiply the probability of the first event
times the probability of the second event after the
first event has occurred.
Example 4
A snack cart has 6 bags of pretzels and 10
bags of chips. Grant selects a bag at
random, and then Iris selects a bag at
random. What is the probability that
Grant will select a bag of pretzels and Iris
will select a bag of chips?
Example 4 Continued
P(pretzel and chip) = P(pretzel) • P(chip after pretzel)
Grant selects one of 6 bags of
pretzels from 16 total bags.
Then Iris selects one of 10
bags of chips from 15 total
bags.
The probability that Grant selects a bag of
pretzels and Iris selects a bag of chips is .
“What do you get if a bunch of
bad guys fall in the ocean?”