Dr. Fowler AFM Unit 7-8 Probability. Copyright © 2012 Pearson Education, Inc. Publishing as...
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Transcript of Dr. Fowler AFM Unit 7-8 Probability. Copyright © 2012 Pearson Education, Inc. Publishing as...
![Page 1: Dr. Fowler AFM Unit 7-8 Probability. Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.](https://reader035.fdocuments.in/reader035/viewer/2022081515/5697bf851a28abf838c879b6/html5/thumbnails/1.jpg)
Dr. Fowler AFM Unit 7-8
Probability
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Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
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Classical (or theoretical) probability is used when each outcome in a sample space is equally likely to occur.
Classical Probability
Example: A die is rolled. Find the probability of Event A: rolling a 5.
There is one outcome in Event A: {5}
1 0.1676
P(A) = “Probability of Event A.”
P(Event) = the favorable number of outcomes the number of possible outcomes
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Empirical (or statistical) probability is based on observations obtained from probability experiments. The empirical frequency of an event E is the relative frequency of event E.
Empirical Probability
Example:A travel agent determines that in every 50 reservations she makes, 12 will be for a cruise.What is the probability that the next reservation she makes will be for a cruise?
Frequency of Event ( ) Total frequency
EP E
12 0.2450
P(cruise) =
fn
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Definition – a probability model will always have:1) positive values & 2) total values adding up to 1
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E = All outcomes with 2 Boys & 1 Girl = { BBG, BGB, GBB } = 3 Total
Calculate the probability that in a 3 child family there are 2 boys and 1 girl. Assume equally likely outcomes.
S = 8 Total outcomes listed
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Example: You roll a die. Find the probability that you roll a number less than 3 or a 4.
The events are mutually
exclusive.P (roll a number less than 3 or roll a 4)
= P (number is less than 3) + P
(4)
2 1 3 0.56 6 6
The Addition Rule – Mutually Exclusive
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The Addition Rule – Not Mutually Exclusive
Example:A card is randomly selected from a deck of cards. Find the probability that the card is a Jack or the card is a heart. The events are not mutually exclusive because
the Jack of hearts can occur in both events.
P (select a Jack or select a heart)
= P (Jack) + P (heart) – P (Jack of
hearts)4 13 152 52 52
1652
0.308
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Complementary EventsThe complement of Event E is the set of all outcomes in the sample space that are not included in event E. (Denoted E′ and read “E prime.”)
P(E) + P (E′ ) = 1
Example: There are 5 red chips, 4 blue chips, and 6 white chips in a basket. Find the probability of randomly selecting a chip that is not blue.
P(E) = 1 – P (E′ ) P (E′ ) = 1 – P(E)
P (selecting a blue chip) 4 0.26715
P (not selecting a blue chip) 4 111 0.73315 15
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On the local news the weather reporter stated that the probability of rain tomorrow is 30%. What is the probability that it will not rain?
no rain 1 rain 1 0.3 0.7 70%P P
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Example:A die is rolled and two coins are tossed. Find the probability of rolling a 5, and flipping two tails.
Multiplication Rule
P (rolling a 5) = 1.6
Whether or not the roll is a 5, P (Tail ) = so the events are independent.
1,2
P (5 and T and T ) = P (5)· P (T )· P (T ) 1 1 16 2 2
124
0.042
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Excellent Job !!!Well Done
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Stop NotesDo Worksheet
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Introduction to Probability:https://www.youtube.com/watch?v=YWt_u5l_jHs
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Consider the experiment of drawing a card from a standard 52 card deck of playing cards (ace through king, four suits). Let E represent the event “draw a heart” and let F represent the event “draw an ace”.
13 and 4n E n F
(a) The word "and" means intersection so and
is 1 (The ace of hearts)
n E F
n E F
(b)The word “OR” means Union, so n (E or F) = 16 (all 13 hearts + ace of clubs + ace of diamonds + ace of spades).
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Consider the experiment of drawing a card from a standard 52 card deck of playing cards (ace through king, four suits). Let E represent the event “draw a heart” and let F represent the event “draw an ace”.
13 1(c)
52 4P E 4 1
52 13P F
1(d)
52
n E FP E F
n S
1n E F
16n E F
16 4(e)
52 13
n E FP E F
n S
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Notice – sum of probabilities is 1
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Notice – sum of probabilities is 1
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What is the probability that in a group of 10 people at least 2 people have the same birthday? Assume that there are 365 days in a year.
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