I was able to answer a, b, and c, but I need help with d and e. Calculate probab
ID: 3394146 • Letter: I
Question
I was able to answer a, b, and c, but I need help with d and e.
Calculate probabilities from the following frequency table.
A1
A2
A3
A4
Total
B1
14
26
13
35
88
B2
39
26
4
75
144
B3
0
5
65
47
117
Total
53
57
82
157
349
Exercises: a. Pr(A4)= 157/349 = 0.4498
b. Pr(not B1)= 349-88 = 261/349 = 0.7478
c. Pr(A4 and B1)= (157+88-35) = 210/349 = 0.6017
d. Pr(A4 or B1)=
e. Pr(A4 given B1)=
A1
A2
A3
A4
Total
B1
14
26
13
35
88
B2
39
26
4
75
144
B3
0
5
65
47
117
Total
53
57
82
157
349
Explanation / Answer
The way Pr(A4 and B1) is calculated in wrong. Because there are only 35 observations which are common to both A4 and B1. So Pr(A4 and B1)= 35/ 349 = 0.1003, it's not 0.6017.
Pr(A4 or B1)= Pr(A4) + Pr(B1)-Pr(A4 and B1); Now, Pr(not B1)=0.7478. So Pr(B1)=1-Pr(not B1)=1-0.7478=0.2522. and Pr(A4 and B1) = 35 / 349 = 0.1003. So Pr(A4 or B1)=0.4498+0.2522-0.1003= 0.6017 (answer);
Pr(A4 given B1) = Pr(A4 and B1) / Pr(B1) = 0.1003 / 0.2522 = 0.3977
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