1
IMPORTANT PROBABILITY RULES ILLUSTRATE
D
Solutions to the wrapup problems  Probability
1)
A die is rolled once. Each number is equally likely to face up. Find the probabilities of the
following events.
a)
The number facing up is 6
b)
The number facing up is not 6
c)
The number facing up is odd
d)
The number facing up is less than 4
e)
The number facing up is odd or is less than 4
f)
The number facing up is odd or is even
SOLUTION
Define the events symbolically
A = {6}
B = {1, 3, 5}
C = {1, 2, 3}
D = {2, 4, 6}
Calculate probability of each event above by summing up their constituent
simple events
a)
P (A) = 1/6
b)
We are looking for the complement of A. The complement rule states:
6
/
5
6
/
1
1
)
A
(
P
1
)
A
(
P
=
=
=
c)
P (B) = 1/6 + 1/6 + 1/6 = 3/6= ½
d)
P (C) = 1/6 + 1/6 + 1/6) = 3/6= ½
e)
P (B U C) = P (B) + P(C) – P (B
∩
C)
= ½ + ½  2/6 = 2/3
Note that {1, 3} are common to B and C.
f)
P (B U D) = P (B) + P (D)
note
that B and D are mutually exclusive
= ½
+ ½ = 1
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2)
60% check email in the first hour of work.
70% check email in the last hour of work
4
0% check email in the first and last hour of work
Find the probability that a worked selected randomly will check email in the first hour or last
hour of work or both.
SOLUTION
Try it yourself! First define the relevant events and then use the additive rule. Are the relevant
events mutually exclusive?
3)
Hospital records show that 12% of all patients are admitted for surgical treatment, 16% are
admitted for obstetrics, and 2% receive both obstetrics and surgical treatment.
If a new patient is
admitted to the hospital, what is the probability that the patient will be admitted either for
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 Fall '11
 Kim
 Conditional Probability, Probability, Mexico City

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