4. Probability II
Sample space : all the possible outcomes
the number of ways achieving success
the total number of possible outcomes
Event: the set of outcomes that fulfils a given
condition
5. Probability of an event A =
the number of ways achieving success
the total number of possible outcomes
n( A)
P ( A)
n( S )
6. 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’
n( A' )
P ( A' )
n( S )
P( A' ) 1 P( A)
7. The Probability of the
Combined Event
Two types of combinations
i. Event A or event B
- is the union of set A and set B
i. Event A and event B
- the intersection of set A and set B
8. 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
10. Sample space
S= T ,1 , (T ,2), (T ,3), (T ,4), (T ,5), (T ,6),
( H ,1), ( H ,2), ( H ,3), ( H ,4), ( H ,5), ( H ,6)
n(S) = 12
A is an event obtaining a ‘4’ and a ’head’
A = (H,4) n( A) = 1
P(A) = n ( A) = 1
n( S ) 12
11. c. Find the probability of obtaining an even
number and a tail.
B is an even number and a tail.
3 1
B= (T,2),(T,4),(T,6) 4
12
P(B) = n ( B )
n( S )
= 3 1
12 4
12. Three coins are tossed.
a.List all the sample space
b. Find the probability of getting 2 heads and a
tail
14. 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.
15.
16. 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?
18. 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.
19. 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
