intoduction to probability
TRANSCRIPT
-
7/30/2019 Intoduction to probability
1/19
-
7/30/2019 Intoduction to probability
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.
-
7/30/2019 Intoduction to probability
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.
-
7/30/2019 Intoduction to probability
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.
-
7/30/2019 Intoduction to probability
5/19
The terms we will use are impossible, very
unlikely, unlikely, evens, likely, very likely
and certain.
-
7/30/2019 Intoduction to probability
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.
-
7/30/2019 Intoduction to probability
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?
-
7/30/2019 Intoduction to 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.
-
7/30/2019 Intoduction to probability
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 =
-
7/30/2019 Intoduction to probability
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 .
-
7/30/2019 Intoduction to probability
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.
-
7/30/2019 Intoduction to probability
12/19
-
7/30/2019 Intoduction to probability
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.
-
7/30/2019 Intoduction to probability
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?
-
7/30/2019 Intoduction to probability
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)
-
7/30/2019 Intoduction to probability
16/19
Outcome number Coin 1 Coin 2 Coin 31 Head Head Head2 Head Head Tail345678
-
7/30/2019 Intoduction to probability
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.
-
7/30/2019 Intoduction to probability
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%
-
7/30/2019 Intoduction to probability
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