I was able to answer a b and c but I need help with d and e

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)=

Solution

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