Warm-up (AP Stats)
Name_________________________________
1.
Describe the sample space. A basketball player shoots three free throws. You record the sequence of hits and
misses.
2.
All human blood can be typed as one of O, A, B, or AB, but the distribution of the types varies a bit with race. Here
is the distribution of blood types for randomly chose black Americans.
Blood type
Probability
3.
O
0.49
A
0.27
B
0.2
AB
?
a.
What is the probability of type AB blood?
b.
Maria has type B blood. She can safely receive blood transfusions from people with blood types O and B.
What is the probability that a randomly chosen black American can donate blood to Maria?
The distribution known as Benford’s law is shown below. Let event B = first digit is 6 or greater, event C = first
digit is odd, and event D = first digit is less than 4.
First Digit
Probability
a.
P( D)
b.
P( B  D)
c.
P( D c )
d.
P(C  D)
e.
P( B  C )
1
0.301
2
0.176
3
0.125
4
0.097
5
0.079
6
0.067
7
0.058
8
0.051
9
0.046
4.
A general can plan a campaign to fight one major battle or three small battles. He believes that he has a probability
of 0.6 of winning the large battle and probability of 0.8 of winning each of the small battles. Victories or defeats in
the small battles are independent. The general must win either the large battle or all three small battles to win the
campaign. Which strategy should he choose?
5.
An athlete suspected of having used steroids is given two tests that operate independently of each other. Test A
has probability 0.9 of being positive if steroids have been used. Test B has probability 0.8 of being positive if
steroids have been used. What is the probability that neither test is positive if steroids have been used?
6.
The table below shows the marital status of adult women broken down by age group.
Married
Never
Married
7.
18-29
30-64
Over 65
Total
7,842
43,808
8,270
59,920
13,930
7,184
751
21,865
Widowed
36
2,523
8,385
10,944
Divorced
704
9,174
1,263
11,141
22,512
62,689
18,669
103,870
a.
Find P(Never married)
b.
Find P(Married or widowed)
c.
Find P(Divorce or 30 to 64)
d.
Find the probability that a person who is 30-64 was never married.
e.
Find P(Widowed  Divorced)
f.
Find P(Widowed  Divorced)
g.
Find P(Married  over 65)
h.
Find P(not divorce)
Choose an employed person at random. Let A be the event that the person chosen is a woman, and B the event that
the person holds a managerial or professional job. Government data tell us that P(A) = 0.46 and the probability of
managerial and professional jobs among women is P(B|A)=0.32. Find the probability that a randomly chosen
employed person is a woman holding a managerial or professional position.