March 09, 2017
HF:
(13.2)Pg.927: 6 - 17ab
AND
WS(13.1) and (13.2)
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March 09, 2017
(13.5) Probabilities of Independent and Dependent Events
Objective: To Find Probabilities of Independent and Dependent Events
To find probabilities of events given the occurence of other events
(Conditional Probability).
Why: This allow us to find more sophisticated probabilities.
March 09, 2017
Obj: To Find Probabilities of Independent and Dependent Events.
Compound Event:
To find probabilities of events given the occurence of other
events (Conditional Probability).
* event consisting of 2 or more simple events.
* can be INDEPENDENT or DEPENDENT
INDEPENDENT: the outcome/probability of one does NOT affect the
outcome/probability of the the other.
DEPENDENT: the outcome/probability of one event DOES change the
outcome/probability of the other event.
March 09, 2017
Obj: To Find Probabilities of Independent and Dependent Events.
To find probabilities of events given the occurence of other
events (Conditional Probability).
Ex.1: Identify whether the events are independent or dependent.
a. One coin is tossed, and then a second coin is tossed.
b. Student names are placed in a bag, one name is chosen and not replaced,
and then a second name is chosen.
c. A card is selected from a deck of cards and put back. Then a second card
is selected.
d. Ann selects a shirt from her closet to wear on Monday and then a different
shirt to wear on Tuesday.
If you replace the object each time, then the events are ________________
If you don't replace the object each time, then the events are ____________
March 09, 2017
Obj: To Find Probabilities of Independent and Dependent Events.
To find probabilities of events given the occurence of other
events (Conditional Probability).
Probability of Two INDEPENDENT Events:
P(A and B) = P(A) P(B)
A
B
P(A and B)
March 09, 2017
Obj: To Find Probabilities of Independent and Dependent Events.
Ex.2
To find probabilities of events given the occurence of other
events (Conditional Probability).
a. Michelle and Chris are going out to lunch. They put 5 green
slips of paper and 6 red slips of paper into a bag. If a person
draws a green slip, they will order a hamburger. If they draw a
red slip, they will order pizza.
Suppose Michelle draws a slip. Not liking the outcome, she puts it
back and draws a second time. What is the probability that
Michelle draws a green slip on each of her draws?
b. A coin is tossed and a die is rolled. What is the probability that
the coin lands heads up and the number rolled is a 6?
March 09, 2017
Obj: To Find Probabilities of Independent and Dependent Events.
To find probabilities of events given the occurence of other
events (Conditional Probability).
Probability of Two DEPENDENT Events:
P(A and B) = P(A) P(B A)
Conditional Probability:
P(B A) is read "the probability that event B occurs given that
event A has already occured" or "the probability of B,
given A".
March 09, 2017
Obj: To Find Probabilities of Independent and Dependent Events.
To find probabilities of events given the occurence of other
events (Conditional Probability).
Ex.3 (Refer to Ex.2 with the green and red slips)
Suppose Michelle draws a slip and does not put it back. Then
her friend Chris draws a slip. What is the probability that both
draw a green slip?
P(A and B) = P(A) P(B A)
Check by doing a tree diagram:
G
Outcomes
R
March 09, 2017
Obj: To Find Probabilities of Independent and Dependent Events.
To find probabilities of events given the occurence of other
events (Conditional Probability).
Conditional probabilities can also be used when additional information is known
about an event.
Ex.
Suppose a die is rolled and it is known that the number rolled is odd. What is
the probability that the number rolled is a 5?
March 09, 2017
Obj: To Find Probabilities of Independent and Dependent Events.
To find probabilities of events given the occurence of other
events (Conditional Probability).
The conditional probability of B given A is:
P(A and B)
P(B A) =
P(A)
March 09, 2017
Obj: To Find Probabilities of Independent and Dependent Events.
Ex.4
To find probabilities of events given the occurence of other
events (Conditional Probability).
Mr. Monroe is organizing the gym class into two teams. The 20 students
randomly draw cards numbered from 1 to 20.
*Students who draw odd are on the Red team.
*Students who draw even are on the Blue team.
a. If Monica is on the Blue team, what is the probability that she drew the
number 10?
March 09, 2017
Obj: To Find Probabilities of Independent and Dependent Events.
To find probabilities of events given the occurence of other
events (Conditional Probability).
b. If two dice are rolled, what is the probability that one die is
a 4, given that the sum of the two die is 9?
March 09, 2017
Obj: To Find Probabilities of Independent and Dependent Events.
To find probabilities of events given the occurence of other
events (Conditional Probability).
HF:
(13.5) Pg.951: 6-19
and
WS(13.5)
ALEKS due Friday @ midnight!
*Weekly Goal = 173 topics
*Quarter Goal = 191 topics