MATH 166 Spring 2016
1.4
c
Wen
Liu
1.4 Basics of Probability
Definition: If S is a finite uniform sample space and E is any event, then the probability of E,
P (E), is given by
Number of elements in E
n(E)
P (E) =
=
Number of elements in S
n(S)
Examples:
1. If a card is drawn at random from a standard 52-card deck, what is the probability that the
card drawn is one of the following?
(a) A king is drawn.
(b) A heart is drawn.
(c) A red card is drawn.
2. Assume that all elementary events in the same sample space are equally likely. A family has
three children. Assuming a boy is as likely as a girl to have been born, what are the following
probabilities?
(a) Three are boys and none are girls.
(b) At least 1 is a boy.
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MATH 166 Spring 2016
1.4
c
Wen
Liu
3. A fair coin is flipped and it is noted whether heads or tails show. A fair 20-sided die is tossed
and the number on the bottom face is noted. What is the probability of the event ”heads shows
on the coin and an even number on the die”?
4. In an attempt to study the leading causes of airline crashes, the following data were compiled
from records of airline crashes (excluding sabotage and military action): Assume that you have
just learned of an airline crash and that the data give a generally good indication of the causes
of airplane crashes. Give an estimate of the probability that the primary cause of the crash
was due to flight crew or bad weather.
5. Let S = {s1 , s2 , s3 , s4 , s5 , s6 } be the sample space associated with the experiment having the
following probability distribution.
(a) Find the probability of A = {s1 , s3 }.
(b) Find the probability of B = S.
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MATH 166 Spring 2016
1.4
c
Wen
Liu
6. The sample space S = {s1 , s2 , s3 } has the property that P (s1 ) + P (s2 ) = 0.46 and P (s2 ) +
P (s3 ) = 0.79. Find the probability of P (s1 ).
7. A pair of fair 6-sided dice is rolled. What is the probability of each of the following?
(a) the sum of the numbers shown uppermost is less than 7
(b) at least one 4 is cast
8. In a survey conducted by a business-advisory firm of adults 18 years old and older in June
2009, during the “Great Recession,” the following question was asked: How long do you think
it will take to recover your personal net worth? The results of the survey follow.
(a) Determine the empirical probability distribution associated with these data.
(b) If a person who participated in the survey is selected at random, what is the probability
that he or she expects that it will take 5 or more years to recover his or her personal net
worth?
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