Intoduction to probability

7/30/2019 Intoduction to probability

1/19


2/19

Understand and use the vocabulary of

probability and the probability scale

Understand and use estimates or measures of

probability List all outcomes for single events, and for

two successive events, in a systematic way

and derive related probabilities.


3/19

Probability is about estimating how likely

(probable) something is to happen.

Probability can be used to predict, for

example, the outcome when throwing a die(dice) or tossing a coin.


4/19

We often use words to describe how probable

we think it is that an event will take place.

For example, we might say that it is likely to

be sunny tomorrow, or that it is very unlikelyto snow in Malaysia.

The words we use can be placed in a

Probability Scale.


5/19

The terms we will use are impossible, very

unlikely, unlikely, evens, likely, very likely

and certain.


6/19

You buy a lottery ticket and win the jackpot.

You toss a coin and get tails.Christmas will fall on 25 December this year.

You throw a die and get 6

It will rain in the last week of May.


7/19

Now think up your own examples to fit each

of the terms in the scale.

Ask a number of students to choose the best

term to describe your examples. Doeseveryone agree?

Do you think these terms are a good way to

describe probability?


8/19

In Maths we need to be more precise about

how likely something (an outcome) is to

happen.

The probability of an outcome can have anyvalue between 0 (impossible) and 1 (certain).

It may be a fraction, decimal or percentage.


9/19

When different outcomes of an event are

equally likely (for example, getting a 6 when

you throw a die), you can use a formula to

calculate the probability of outcomes.

Probability of an outcome =


10/19

If you toss 2 coins there are four possible

outcomes - 2 heads, a head and a tail, a tail

and a head and 2 tails.

This means that the probability of getting 2heads is 1/4 or 0.25 or 25%. Notice that

there are 2 ways of getting a head and a tail

so the probability of this outcome is 2/4 or

or 0.5 or 50%. The other outcome is 2 tails with a

probability of .


11/19

If we add the probabilities of all the possible

outcomes together the total is 1 (0.25 + 0.5 +

0.25). The sum of the probabilities of all the

different outcomes will always equal 1.


12/19


13/19

Notice that in order to make all outcomes

equally probable we need to use a fair die

and to choose a card without looking.

Also if you add the probabilities of 2 and 3the answer = 1.

This is always true the probability of

something happening + the probability of it

not happening always equals 1.


14/19

What is the probability of choosing a card

from a pack which is not a queen?

What is the probability of throwing an odd

number with a fair six-sided die?


15/19

These are relatively simple examples. When

things get more complicated it is necessary

to list all outcomes systematically.

For example if we throw three coins whatare the different outcomes?

Complete the following table and work out

the probability of getting two heads and a

tail (in any order)


16/19

Outcome number Coin 1 Coin 2 Coin 31 Head Head Head2 Head Head Tail345678


17/19

You can estimate probabilities from

experiment by repeating an event a number

of times and recording the outcomes.

The more times you repeat the moreaccurate your estimate will be.


18/19

You drop a drawing pin from the same height

1000 times.

The pin lands up 324 times.

The pin lands down 676 times. The probability of the pin landing up =

324/1000 = 32.4%


19/19

100 footballs are checked and 20 are found

to have punctures. Calculate the probability

of a football having a puncture when chosen

at random.

The probability = number of footballs with

punctures/total number of footballs

= 20/100 = 0.2

Intoduction to probability

Documents

Transcript of Intoduction to probability