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Probability
1. I have a loaded die. The distribution is listed below.
Face
p(x)
1
0.3
2
0.1
3
0.1
4
0.1
5
0.1
6
0.3
If this die is thrown and the top shows an odd number what is the probability that the number is1?
2. In an eye clinic, women ages 30-39 was measured for unaided distance vision in both the right eye
and the left eye and the results are shown in the table below.
Right Eye
Highest
Second
Third
Lowest
Highest
750
125
60
2
Left Eye
Second
130
775
180
40
Third
60
210
885
90
Lowest
35
40
100
25
a. What is the probability that the right eye was high?
b. What is the probability that the right eye and the left eye were both at the lowest
c. What is the probability that the left eye is third given that the right eye was third
3. Two dice are rolled. Find the probabilities that
a.
b.
c.
d.
the white die is an odd number.
the sum of the two dice is 6
both dice show odd numbers
the number on the black die is larger that the number on the white die.
4. If P(A) = 0.3 and P(B) = 0.4, and A and B are mutually exclusive events, find the P(A or B). What is
the P(Aand B)?
5. If P(A) = 0.2 and P(B) = .6, and P(A|B) = .1, find the P (A or B) . (A & B are not mutually ex)
6. If two poker chips are drawn from a box that contains one red, one blue, and one white chip
without replacement, what is the probability of drawing one red and one blue chip?
7. Two flower seeds are randomly selected from a package that contains five seeds for red flowers
and three seeds for white flowers. What is the probability that both seeds are for white flowers?
8. A company that manufactures shoes has three factories. Factory 1 produces 25% of the
company’s shoes. Factory 2 produces 60%, and Factory 3 produces 15%. One percent of the shoes
produced by Factory 1 are mislabeled, 0.5% of those produced by Factory 2 are mislabeled, and 2%
of those produced by Factory 3 are mislabeled. If you purchase one pair of shoes manufactured
by this company and they were mislabeled, what is the probability that they came from Factory 1?