WHAT WILL HAPPEN IN 2012?

WHICH TEAM WILL WIN WORLD CUP 2010?

CHAPTER 7 :PROBABILITY

Probability II

Sample space : all the possible outcomes

Event: the set of outcomes that fulfils a given condition

outcomes possible ofnumber totalthe

success achieving waysofnumber the

)(

)()(

Sn

AnAP

Probability of an event A =

outcomes possible ofnumber totalthe

success achieving waysofnumber the

The Probability of A Complement Event The complement of an event A

- is the set of all outcomes in the sample space that are not included in the outcomes of event A and is written as A’

)(

)'()'(

Sn

AnAP

)(1)'( APAP

The Probability of the Combined Event

Two types of combinationsi. Event A or event B - is the union of set A and set Bii. Event A and event B - the intersection of set A and set

B

Finding the probability by Listing the outcomes

A fair coin is tossed and a fair dice is rolled.a. List all the possible outcomes. * You can draw a tree diagram.*b. Find the probability of obtaining a ‘4’

and a ’head’c. Find the probability of obtaining an even

number and a tail

T

H

1

2

3

4

5

6

1

2

3

4

5

6

Sample space S=

n(S) = 12 A is an event obtaining a ‘4’ and a

’head’ A = (H,4) n( A) = 1 P(A) = =

)6,(),5,(),4,(),3,(),2,(),1,(

),6,(),5,(),4,(),3,(),2,(,1,

HHHHHH

TTTTTT

)(

)(

Sn

An12

1

c. Find the probability of obtaining an even number and a tail.

B is an even number and a tail. B= (T,2),(T,4),(T,6) P(B) =

=

4

1

12

3

)(

)(

Sn

Bn

4

1

12

3

Three coins are tossed.a.List all the sample spaceb. Find the probability of getting 2

heads and a tail

Tree diagram

Finding the probability by Listing the outcomes

There are 3 balls in a bag: red, yellow and blue. One ball is picked out, and not replaced, and then another ball is picked out.

Finding the probability by Listing if you throw two dice, what is the

probability that you will get the sum of the two numbers is :

a) 8, b) 9, c) either 8 or 9?

Sample Space of a combined event

Probability II

Independent and Dependent Events

Suppose now we consider the probability of 2 events happening. For example, we might throw 2 dice and consider the probability that both are 6's.

We call two events independent if the outcome of one of the events doesn't affect the outcome of another. For example, if we throw two dice, the probability of getting a 6 on the second die is the same, no matter what we get with the first one- it's still 1/6.

Probability II

On the other hand, suppose we have a bag containing 2 red and 2 blue balls. If we pick 2 balls out of the bag, the probability that the second is blue depends upon what the colour of the first ball picked was. If the first ball was blue, there will be 1 blue and 2 red balls in the bag when we pick the second ball.

So the probability of getting a blue is 1/3. However, if the first ball was red, there will be 1 red and 2 blue balls left so the probability the second ball is blue is 2/3. When the probability of one event depends on another, the events are dependent

EXERCISE : SPM QUESTIONS