Harry owns shares of stock in both Bidwell Value Company and Mini Car Motors, In
ID: 3150098 • Letter: H
Question
Harry owns shares of stock in both Bidwell Value Company and Mini Car Motors, Inc. Harry has recorded the performance of these shares on each day for a 200 day period as to whether the price has risen, fallen, or remained unchanged. Harry’s data is as follows:
Event
Bidwell
Mini Car
# of days
E1
Rise
Rise
40
E2
Rise
Unchanged
14
E3
Rise
Fall
20
E4
Unchanged
Rise
18
E5
Unchanged
Unchanged
12
E6
Unchanged
Fall
14
E7
Fall
Rise
28
E8
Fall
Unchanged
16
E9
Fall
Fall
38
A) What is the probability of a rise in Bidwell and a fall in Mini Car stock?
B) What is the probability of a rise in Bidwell or a fall in Mini Car stock?
C) Suppose Harry is told that Mini Car stock has fallen. What is the probability that Bidwell stock has risen?
D) Are the events “a rise in Bidwell stock” and “a fall in Mini Car stock” statistically independent?
Event
Bidwell
Mini Car
# of days
E1
Rise
Rise
40
E2
Rise
Unchanged
14
E3
Rise
Fall
20
E4
Unchanged
Rise
18
E5
Unchanged
Unchanged
12
E6
Unchanged
Fall
14
E7
Fall
Rise
28
E8
Fall
Unchanged
16
E9
Fall
Fall
38
Explanation / Answer
Two-Way Table
Count of Bidwell
Mini Car
Bidwell
Fall
Rise
Unchanged
Grand Total
Fall
1
1
1
3
Rise
1
1
1
3
Unchanged
1
1
1
3
Grand Total
3
3
3
9
A) What is the probability of a rise in Bidwell and a fall in Mini Car stock?
P=1/9
B) What is the probability of a rise in Bidwell or a fall in Mini Car stock?
P=5/9
C) Suppose Harry is told that Mini Car stock has fallen. What is the probability that Bidwell stock has risen?
P=1/3
D) Are the events “a rise in Bidwell stock” and “a fall in Mini Car stock” statistically independent?
P(a rise in Bidwell stock) =3/9 =1/3
P(a rise in Bidwell stock/ a fall in Mini Car stock) =1/3
P(a rise in Bidwell stock) = P(a rise in Bidwell stock/ a fall in Mini Car stock).
Therefore the events “a rise in Bidwell stock” and “a fall in Mini Car stock” are statistically independent.
Two-Way Table
Count of Bidwell
Mini Car
Bidwell
Fall
Rise
Unchanged
Grand Total
Fall
1
1
1
3
Rise
1
1
1
3
Unchanged
1
1
1
3
Grand Total
3
3
3
9
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