More on Probability by David Palay

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In how many ways can the debate team choose a president and a secretary if there are 10 people on the team?

Mrs. Marshall has 11 boys and 14 girls in her class.A. How many ways can she select 2 girls to pass out a

snack?B. How many ways can she select 5 boys to pass out new

books?C. How many ways can she select 3 students to carry a

desk to the office?

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Definition of Experimental Probability:

Definition of Theoretical Probability:

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The Law of Large Numbers says, roughly, that as the number of trials increases,Experimental Probability approaches Theoretical Probability

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What is the probability that a point chosen randomly from within the rectangle will be within the shaded square?

4 in.

7 in.

2 in.

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2 3 4 5 6 7 8 9 10 11 120

5

10

15

20

25

30

4

8 7

14

2527

24

16

10 96

Rolls of 2 six sided dice

Sum

Tota

l occ

urre

nces

The above chart represents the outcome of 150 rolls of 2d6. What is the experimental probability of:

Rolling a 7?Rolling a 10 or higher? Rolling a 9 or Lower?

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Hmmm… Something interesting there about 10 and higher vs. 9 and lower…What do we get when we add them together?

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Interesting…What conclusion can we draw from this?

Compliments Rule

P ( A )+P ( Ac )=1

Combining events

P ( A∪B )=?

Venn Diagrams

Event A

New Symbols!Name Loose

TermsSymbol Example

Union Or

Intersection And

Compliment But Not

A∩B

A∪B

Ac

So how about these?

Addition rule for unions

The probability of A OR B is the Probability of A PLUS the Probability of B MINUS the Probability of A AND B

Mutual Exclusion

Two events are mutually exclusive if:• • There is no overlap• There is no possibility of them happening

together• No outcomes in

common

Change of Pattern

• In the following Venn Diagrams, we often assume that two events, A and B, constitute the entire Universe. That is, there is nothing outside of A and B.

Complimenting complex sets

What is the compliment of

What about ’s compliment?

So, algorithm

Write these on the Board…

The Monty Hall Problem

• Monty Hall, the host of Let’s Make a Deal, used to offer contestants this situation:– There are three doors, behind one is a great prize (Let’s go

with new car for the sake of our example) and behind the other two doors are fake prizes (goats, is the usual example here)

– The contestant is told to pick one door, but not to open it. The Host, Mr. Hall, then would open one of the two other doors to reveal one of the goats.

– The contestant is now given the opportunity to switch his/her choice to the as-yet untouched & unpicked third door.

Extra Practice

The chart describesthe transportation methods for 162travellers.

If a traveller is selected at random, what is the probability that:P(ferry or train)P(ferry or rental car)P(train and ferry, or train and rental car)