Samples of a cast aluminum part are classified on the basis of surface finish (in microinches) and edge finish. The results of 102 parts are summarized as follows: edge finish excellent good surface finish excellent 84 4 good 5 9 Let A denote the event that a sample has excellent surface finish, and let B denote the event that a sample has excellent edge finish. If a part is selected at random, determine the following probabilities. Round your answers to three decimal places (e. g. 98.765). (a) Upper P left-parenthesis Upper A right-parenthesis equalsEntry field with correct answer .8627 (b) Upper P left-parenthesis Upper B right-parenthesis equalsEntry field with correct answer .8725 (c) Upper P left-parenthesis Upper A prime right-parenthesis equalsEntry field with correct answer .1372 (d) Upper P left-parenthesis Upper A intersection Upper B right-parenthesis equalsEntry field with correct answer .8235 (e) Upper P left-parenthesis Upper A union Upper B right-parenthesis equalsEntry field with correct answer .9117 (f) Upper P left-parenthesis Upper A prime union Upper B right-parenthesis equalsEntry field with incorrect answer .9214

a) P (A)= 88/102= 0.8627

(b) P (B)=  89/102= 0.8725

c) P (A`) =  14/102 = 0.1372

(d) P (A∩B) = 84/102 =0.8235

(e) P(AUB)= 93/102 = 0.9117

(f)P (A`UB) = 98/102= 0.96078

Step-by-step explanation:

                                                                   edge                  

                                                  finish excellent       good           Total

(A )surface finish excellent            84                      4                  88

good                                    ( B) ⇵    5                       9                  14

Total                                               89                      13                102

a) Upper P left-parenthesis Upper A right-parenthesis equals

P (A)= 88/102= 0.8627

All the elements of set A = 84+4= 88

(b) Upper P left-parenthesis Upper B right-parenthesis equals

P (B)=  89/102= 0.8725

All the elements of set B = 84+5= 89

c) Upper P left-parenthesis Upper A prime right-parenthesis equal

P (A`) =  14/102 = 0.1372

All the elements of Universal set U which are not elements of set A = 102- 88= 14

(d) Upper P left-parenthesis Upper A intersection Upper B right-parenthesis equals

P (A∩B) = 84/102 =0.8235

Only those elements of set A and set B which are common

(e) Upper P left-parenthesis Upper A union Upper B right-parenthesis equals

P(AUB)= 93/102 = 0.9117

Totalling elements of set A and B= 88+5= 93

(f) Upper P left-parenthesis Upper A prime union Upper B right-parenthesis equals

P (A`UB) = 98/102= 0.96078

All the elements of Universal set U which are not elements of set A and the elements of Set B = 5+9+ 84= 98