10.3 Conditional Prob and Tree Diagrams

Conditional Prob and Tree Diagrams.notebook
February 24, 2016
Conditional Probability:
P(A/B) is the probability of A occurring given that B has already occurred.
Example 1:
A = deal a king on the first card
B = deal a king on the second card
P(B/A) is the probability of dealing a king on the second card given that a king has been dealt on the first card:
P(B/A) = ??
Feb 43:07 PM
Example 2:
A = flip heads on first flip
B = flip heads on 2nd flip
P(B/A) = ??
Feb 43:07 PM
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Conditional Prob and Tree Diagrams.notebook
February 24, 2016
Multiplication Rule:
Example 1:
A = I wear a blue shirt
B = I wear tan pants
P(A) = .25
P(B/A) = .40
1) What does P(B/A) mean?
2) P(A and B) = Feb 43:08 PM
Example 2:
A bowl of jelly beans contains 6 red jelly beans, 7 blue jelly beans, and 7 white jelly beans. I select without replacement . Find the probability I select a) 3 red jelly beans
b) 1 red followed by 1 blue jelly bean.
c) 1 blue jelly bean followed by 1 red jelly bean
d) 1 red and 1 blue jelly bean (in any order).
Feb 43:14 PM
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Conditional Prob and Tree Diagrams.notebook
February 24, 2016
Example 3:
30% of a club are juniors and 70% are seniors.
Of the juniors, 45% are males. Of the seniors, 60% are males.
Find the probability that a randomly selected students is male!
Feb 43:10 PM
Example 4:
30% of a club are juniors and 70% are seniors.
Of the juniors, 45% are males. Of the seniors, 60% are males.
1) Draw a tree diagram representing this scenario.
2) P ( I randomly select a male junior)
3) P(randomly select a male) = 4) P (randomly select a female) = 5) ** Given that I’ve selected a male, what is the probability that he’s a junior?
P(M and JR) = P(M)P(JR/M)
Feb 43:10 PM
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Conditional Prob and Tree Diagrams.notebook
February 24, 2016
Example 5: On days when it snows, the probability that school is closed is 10%. On days when the it does not snow, the probability that the school is closed is 1%. It snows on 5% of school days.
1) Draw a tree diagram.
2) What is the probability that the school is closed today because of snow?
P(snow and closed) = (.05)(.1) = .005 = .5%
3) What is the probability that the school is closed for any reason?
P(closed) = (.05)(.1) + (.95)(.01)= .0145 = 1.45%
4) What is the probability that the school is not closed today?
P(not closed) = 1.0145 = .9855 = 98.55%
**5) Given that school is closed, what is the probabilty that it snowed today? P(closed and snowed) = P(closed)P(snow/closed)
Feb 43:11 PM
WKSHT ANSWERS
1.
.375
2.
.48
3.
.12
4.
a) tree diagram
b) .58
c) .42
d) .8276
5.
a) tree diagram
b) .42
c) .525
d) .475
e) .8
6.
a) tree diagram
b) .48
c) .68
d) .32
e) .7059
Mar 1411:11 AM
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Conditional Prob and Tree Diagrams.notebook
February 24, 2016
BIRTHDAY PROBLEM
Fact: if there are more than 23 people in a room, there is more than a 50% probability that at least 2 people have the same birthday!
Feb 43:15 PM
Feb 1410:34 AM
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