Summary Examples
Example 1
An experiment consists of tossing a die and then flipping a coin once if the die outcome is even.
If the die outcome is odd, the coin is flipped twice.
a)
Describe the sample space by listing its elements.
b)
Describe the sample space using a tree diagram.
Answer:
a)
S = {(1HH), (1HT), (1TH), (1TT), (2H), (2T), (3HH), (3HT), (3TH), (3TT), (4H),
(4T), (5HH), (5HT), (5TH), (5TT), (6H), (6T)}
b)
Example 2
For the sample in example 1:
a)
list the elements of event A: a number less than 3 occurs on the die
A = {(1HH), (1HT), (1TH), (1TT), (2H), (2T)}
b)
list the elements of event B: two tails occur
B = {(1TT), (3TT), (5TT)}
c)
list the elements of event A
′
A
′
= {(3HH), (3HT), (3TH), (3TT), (4H), (4T), (5HH), (5HT), (5TH), (5TT), (6H), (6T)}
d)
list the elements of event A
′∩
B
A
′∩
B = {(3TT), (5TT)}
e)
list the elements of event A
∪
B
4
H
T
6
H
T
2
H
T
1
H
T
H
T
H
T
3
H
T
H
T
H
T
5
H
T
H
T
H
T