Download Mathematics 1050 Some solutions of Homework 5

Mathematics 1050
Some solutions of Homework 5
An unbiased coin is tossed ve times. Find the probability of the event that
the coin lands heads exactly once.
Section 7.4: 2
Solution: Each outcome of the experiment can represented as a sequence of heads and tails.
Using the multiplication principle, we see that the number of outcomes of this experiment
is given by 2 . Let E denote the event that the coin lands heads exactly once. Since there
are C (5; 1) ways this can occur, we see the required probability is
5
5
( ) C (5; 1)
=
=
= :
n(S )
2
32 32
4 Find the probability that the coin lands heads more than once.
( )=
P E
Section 7.4:
5!
n E
4!
5
Let F denote the event that the coin lands heads more than once. Then, F c
is the event that the coin does not land heads, which means that it lands tails ve times.
There are C (5; 5) ways that this occur. Hence
Solution:
(
P F
c
)=
( c)
=
n(S )
n F
C
(5; 5)
1
= :
2
32
5
On the other hand
1
31
= :
32 32
Section 7.4: 10 Four balls are selected at random without replacement from an urn containing 3 white balls and 5 blue balls. Find the probability that they are all blue.
( )=1
P F
(
P F
c
)=1
We have a total of 8 balls. The number of outcomes of this experiment is C (8; 4).
denote that the event that the 4 balls are blue. Then
Solution:
Let E
( )=
P E
1
(5; 4) 5 4 3 2
=
= :
C (8; 4)
8 7 6 5 14
C
1