Probability

Learning Outcomes

I can find the probability of simple events, combined events and use expectation

I can use the addition rule for Mutually exclusive events

I can understand Independent events and determine the probability of 2 independent events occurring

I can use a probability tree to illustrate events

I can understand Dependent events

Probability Probability

Probability is how likely an event is to happen

P(event) = No. of desired outcomes total No. of outcomes

Example:

A dice is thrown. The probability of getting a 3: P(3) =

The probability of an even number P(even) =

1 2 3 4 5 6

1

2

3

4

5

6

Probability Combined Events

Sample space ( A probability space diagram)

Example

Two dice are rolled and the numbers on each dice are added

i) Complete the probability space diagram below

ii) Find a) P(total = 6)

b) P(total is even)

c) P(total ≥ 8)

First die

Sec

ond

die

Probability Mutually Exclusive Events

Head and Tail are mutually exclusive events when a coin is tossed

Mutually exclusive – one or other of the events happen, not both.

Keyword is ‘OR’

Example

Rolling a die- 6 OR not 6:

not getting

)6()6( = 1

Getting a red card- red OR not red: )()( RR = 1

Being sunny today- sun OR no sun: )()( SS = 1

P(event) = 1 – P( )event

Probability Mutually Exclusive Events

Example

1) Rolling a die

P(5 or 6) =

2) Probability of not raining in June given P(rain) = 0.3

P( ) = rain

Probability Independent Events

Events are unrelated

Keyword is ‘AND’

P(A and B) = P(A) x P(B)

P(Rain on a given day) = 0.3 P(Tuesday) = 1/7

P(Rain and Tuesday) =

A coin is tossed and a die is rolled. Find:

P(Head and 6) =

Probability Tree Diagrams

1. A bag has 5 green balls and 4 red balls. Two balls are selected at random with replacement.i. List the 4 possible outcomesii. Find P(2 red)iii. P(1 of each colour)iv. P(2 green)

G

R

G

R

G

R

P(G) = 5/9

P(G) = 5/9

P(G) = 5/9P(R) = 4/9

P(R) = 4/9

P(R) = 4/9

P(2 Red) =

P(1 of each colour) =

P(2 green) =

Probability Tree Diagrams

1. A bag has 5 green balls and 4 red balls. Two balls are selected at random without replacement.i. List the 4 possible outcomesii. Find P(2 red)iii. P(1 of each colour)iv. P(2 green)

G

R

G

R

G

R

ProbabilityTree Diagrams that lead to

quadratic equations

When a piece of toast is dropped it is more likely to land buttered side down. When it is dropped twice the probability that it will only land once buttered side down is 0.48.What is the probability that it will land buttered side down after it is dropped only once?

P(B) Buttered side down

P(B) Buttered side up

B

B

B

B

B

B

Probability Additional Notes

Probability

I can find the probability of simple events, combined events and use expectation

I can use the addition rule for Mutually exclusive events

I can understand Independent events and determine the probability of 2 independent events occurring

I can use a probability tree to illustrate events

I can understand Dependent events

Learning Outcomes:At the end of the topic I will be able to

Can Revise Do Further