# 「∩」「∪」符號代表咩意思???

1.In an experiment we roll a balanced die and observe the total number of points, which are 1, 2, 3, 4, 5 and 6. These are the elements of the sample space. If D={3,4,5} and E={2,4,6} , list the outcomes that comprise each of the following events, and also express the events in words: D', D∪E , D∩E , D'∪E and D'∩E' .

2.Given the mutually exclusive events Y and Z, for whichP(Y)=0.28 andP(Z)=0.47 , find

a.P(Y') ;

b.P(Z')

c.P(Y ∩ Z)

d.P(Y∪ Z)

e.P(Y'∩ Z')

### 3 個解答

• 最佳解答

「∪」是合并的意思而「∩」是相交的意思。「'」是補集或者不屬於

1 D' = {1,2,6} D∪E = {2,3,4,5,6} D∩E = {4} D'∪E = {1,2,4,6}

D'∩E' = {1}

2(a) P(Y') = 1 - 0.28 = 0.72

(b) P(Z') = 1 - 0.47 = 0.53

(c) P(Y ∩ Z) = 0 (as Y and Z are the mutually exclusive events)

(d) P(Y∪ Z) = 0.28 + 0.47 = 0.75

(e) P(Y'∩ Z') = 1 - P(Y) - P(Z) = 1 - 0.28 - 0.47 = 0.25

• A ∪ B means the set of those elements which are either in A, or in B, or in both

A ∩ B means the set that contains all those elements that A and B have in common

Y' means for those not belong to Y.