Additional
Reading
Question #
1 Highlight
the values which are NOT VALID for probabilities
?
0.50
?
-0.10
?
1.10
2 Is a
good hitter in baseball who has struck out the last six times due for a hit his
next time up?
?
Yes the hitter is due for a hit. This is an example of the Law of
Averages
?
This is an example of the so-called Law of Averages. No, the hitter is
not due for a hit because the Law of Averages is non-existent and doesn’t predict anything.
?
Yes, the hitter is due for a hit. This is an example of the Law of Large
Numbers
?
The Law of Large Numbers predicts the hitter is not due for a hit.
3 The
running mean of the relative frequency of the event appears to settle down to a
constant value.
?
This is an example of the Law of Large Numbers.
?
This is an example of the Law of Averages.
http://davidmlane.com/hyperstat/probability.html
https://www.boundless.com/algebra/textbooks/boundless-algebra-textbook/combinatorics-and-probability-343/combinatorics-57/permutations-238-5523/
Sequences
of 4 of 7 things 840
Groups
of 4 of 7 things 35
#
of poker hands 25,98,960
4 The
number of sequences (order is important) formed by drawing without replacement
of 4 things from 8 things=
5 The
number of sequences (order is important) formed by drawing with replacement of 4 things from 8 things=
6 The
number of committees of size 4 formed from 8 people =
https://www.boundless.com/statistics/textbooks/boundless-statistics-textbook/probability-8/probability-rules-34/the-addition-rule-170-4444/
7 P(Democrat
and Republican) > 0
?
Correct
?
Incorrect
8 P(Democrat,
Republican, or Independent) = 0, or impossible
?
Correct
?
Incorrect
9 P(Democrat,
Republican, or Independent) = 1, or certain
?
Correct
?
Incorrect
10 P(Democrat
and Republican) = 0, or impossible
?
Correct
?
Incorrect
toss
of 2nd die
1 2 3 4 5 6
1 2 3 4 5 6 7
2 3 4 5 6 7 8
3 4 5 6 7 8 9
4 5 6 7 8 9 10
5 6 7 8 9 10 11
6 7 8 9 10 11 12
11 Assume the
mutually exclusive events {1,2,3,4,5} occur with the following probabilities:
X P(X = x)
1 0.047
2 0.136
3 0.553
4 0.198
5 0.067
Total 1.000
Which
applies?
?
Simple Multiplication Rule: P(A and B) = P(A)*P(B)
?
Simple Addition Rule: P(A or B) = P(A) + P(B)
?
General Addition Rule: P(A or B) = P(A) + P(B) – P(A and B)
12 P(X
not more than 4) =
13 P(X
at least 3) =
14 P(X
= 2) =
15 P(X
> 1) =
16 P(X
< 6) =
17 P(A) = 0.418
P(B) = 0.242
P(C) = 0.524
P(A and
B)= 0.184 Note: If P(A and B) = 0, A and B are mutually exclusive.
Otherwise, A and B can occur jointly
18 Which
applies?
?
Simple Multiplication Rule: P(A and B) = P(A)*P(B)
?
Simple Addition Rule: P(A or B) = P(A) + P(B)
?
General Addition Rule: P(A or B) = P(A) + P(B) – P(A and B)
19 P(A or B)
=
20 P(A or B
or C) =
http://www.princeton.edu/~achaney/tmve/wiki100k/docs/Statistical_independence.html
https://www.boundless.com/statistics/textbooks/boundless-statistics-textbook/probability-8/probability-rules-34/the-multiplication-rule-171-4445/
http://www.algebralab.org/lessons/lesson.aspx?file=Algebra_ProbabilityMultiplicationRule.xml
P(A) = 0.433
P(B) = 0.348
P(A and
B) = 0.150
21 Are A and
B independent events?
?
Yes
? No
22 How do you
test independence?
23 If each of
the branches on the right of the figure are equally likely, the P(1 purchase)
=
24 Which Rule
applies to the sequence of independent events?
?
Simple Multiplication Rule: P(A and B) = P(A)*P(B)
?
Simple Addition Rule: P(A or B) = P(A) + P(B)
?
General Addition Rule: P(A or B) = P(A) + P(B) – P(A and B)
Assume
the following probabilities:
P(customer
makes purchase) =0.887
P(customer
does not purchase) = 0.113
Event Purchases Probability
25 neither
purchases 0
26 both
purchase 2
27 one
xor other purchases 1
(0,1,or
2) 0.000
28 Explain
why P(Purchases = 0, 1, or 2) = 1
29 Fill in
the blanks in the following relative frequency contingency table for events A,
B, C, D, E
A B C
D 0.25 0.17 0.62
E 0.14 0.13 0.11
0.33 0.28 0.80
30 Compute
the marginal probabilities for following summary of poll results,
Republican Democrat Independent
Male 0.611 0.003 0.048
Female0.126 0.125 0.088
31 P(Male and
Republican) is type
?
Joint
?
Marginal
?
Conditional
32 P(Male and
Republican)=
33 P(Male) is
type
?
Joint
?
Marginal
?
Conditional
34 P(Male) =
35 P(Male |
Republican) is type https://www.youtube.com/watch?v=H02B3aMNKzEhttps://people.richland.edu/james/lecture/m170/ch05-rul.html
?
Joint
?
Marginal
?
Conditional
36 P(Republican
| Male)= (Compute
using the values in the Male row)
37 P(Male |
Republican) = (Compute
using the values in the Republican column)
