Warm Up
description
Transcript of Warm Up
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Material Taken From:
Mathematicsfor the international student
Mathematical Studies SL
Mal Coad, Glen Whiffen, John Owen, Robert Haese, Sandra Haese and Mark Bruce
Haese and Haese Publications, 2004
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Warm Up
• In a group of 108 people in an art gallery 60 liked the pictures, 53 liked the sculpture and 10 liked neither.
• What is the probability that a person chosen at random liked the pictures but not the sculpture?
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• BrainPop Video–Compound Events
Section 14K – Laws of Probability
• Sometimes events can happen at the same time.• Sometimes you will be finding the probability of
event A or event B happening.• Sometimes you will be finding the probability of
event A and event B happening.
Today:
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Laws of ProbabilityType Definition FormulaMutually Exclusive Events
Combined Events(a.k.a. Addition Law)
Conditional Probability
Independent Events
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Mutually Exclusive Events
• A bag of candy contains 12 red candies and 8 yellow candies.
• Can you select one candy that is both red and yellow?
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Laws of ProbabilityType Definition FormulaMutually Exclusive Events
events that cannot happen at the same time
P(A ∩ B) = 0 P(A B) = P(A) + P(B)
Combined Events(a.k.a. Addition Law)
Conditional Probability
Independent Events
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P(either A or B) = P(A) + P(B)
)()()( BPAPBAP
Mutually Exclusive Events
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Example 1) Of the 31 people on a bus tour, 7 were born in Scotland and 5 were born in Wales.
a) Are these events mutually exclusive?b) If a person is chosen at random, find the
probability that he or she was born in:i. Scotlandii. Walesiii. Scotland or Wales
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Laws of ProbabilityType Definition FormulaMutually Exclusive Events
events that cannot happen at the same time
P(A ∩ B) = 0 P(A B) = P(A) + P(B)
Combined Events(a.k.a. Addition Law)
events that can happen at the same time
P(AB) = P(A) + P(B) – P(A∩B)
Conditional Probability
Independent Events
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P(either A or B) = P(A) + P(B) – P(A and B)
)()()()( BAPBPAPBAP
Combined Events
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Example 2) 100 people were surveyed:
• 72 people have had a beach holiday• 16 have had a skiing holiday• 12 have had both
What is the probability that a person chosen has had a beach holiday or a ski holiday?
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Example 3) If P(A) = 0.6 and P(A B) = 0.7 and P(A B) = 0.3, find P(B).
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Conditional ProbabilityTen children played two tennis matches each.
Child First Match Second Match
1 Won Won2 Lost Won3 Lost Won4 Won Lost5 Lost Lost6 Won Lost7 Won Won8 Won Won9 Lost Won10 Lost Won
What is the probability that a child won his first match, if it is known that he won his second match?
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Laws of ProbabilityType Definition FormulaMutually Exclusive Events
events that cannot happen at the same time
P(A ∩ B) = 0 P(A B) = P(A) + P(B)
Combined Events(a.k.a. Addition Law)
events that can happen at the same time
P(AB) = P(A) + P(B) – P(A∩B)
Conditional Probability
the probability of an event A occurring, given that event B occurred
P (A | B) = P (A ∩ B) P (B)
Independent Events
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Example 4) In a class of 25 students, 14 like pizza and 16 like iced coffee. One student likes neither and 6 students like both.
One student is randomly selected from the class. What is the probability that the student:
a) likes pizzab) likes pizza given that he/she likes iced coffee?
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Example 5) In a class of 40, 34 like bananas, 22 like pineapples and 2 dislike both fruits.
If a student is randomly selected find the probability that the student:
a) Likes both fruitsb) Likes bananas given that he/she likes pineapplesc) Dislikes pineapples given that he/she likes bananas
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Example 6) The top shelf of a cupboard contains 3 cans of pumpkin soup and 2 cans of chicken
soup. The bottom self contains 4 cans of pumpkin soup and 1 can of chicken soup.
Lukas is twice as likely to take a can from the bottom shelf as he is from the top shelf . If he takes one can without looking at the label, determine the probability that it:
a) is chickenb) was taken from the top shelf given that it is chicken
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Independent Events
• If one student in the class was born on June 1st can another student also be born on June 1st?
• If you roll a die and get a 6, can you flip a coin and get tails?
Section 14L – Independent Events
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Laws of ProbabilityType Definition FormulaMutually Exclusive Events
events that cannot happen at the same time
P(A ∩ B) = 0 P(A B) = P(A) + P(B)
Combined Events(a.k.a. Addition Law)
events that can happen at the same time
P(AB) = P(A) + P(B) – P(A∩B)
Conditional Probability
the probability of an event A occurring, given that event B occurred
P (A | B) = P (A ∩ B) P (B)
Independent Events occurrence of one event does NOT affect the occurrence of the other
P(A ∩ B) = P(A) P(B)
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Find p if:a) A and B are mutually exclusiveb) A and B are independent
P (A) = ½ P (B) = 1/3 and P(A B) = p
Example 7)
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Homework
• Worksheet: • 16I.1 #1-4 all• 16I.2 #1, 3, 5, 6, 7
• 16J