Suppose that we have a sample space S5 {E1, E2, E3, E4E4E, E5, E6, E7}, where E1, E2, . . ., E7 denote the sample points. The following probability assignments apply: P(E1) 5 .05, P(E2) 5 .20, P(E3) 5 .20, P(E4) 5 .25, P(E5) 5.15, P(E6) 5 .10, and P(E7) 5 .05. LetA5{E1,E4E4E, E6}B5{E2E2E, E4E4E, E7E7E}C5{E2E2E, E3,E5,E7E7E}a. Find P(A(A(), P(B), and P(C).b. Find AB and P(A(A(>B).d. Are events A and C mutually exclusive?C mutually exclusive?Ce. Find Bc and P(Bc).

P(A) = 0.4 ; P(B) = 0.50 ; P(C) = 0.60 ; P(A u B) = 0.65 ; P(A n B) = 0.25 ;

A and C are mutually exclusive ;

0.5

Step-by-step explanation:

S = {E1, E2, E3, E4, E5, E6, E7}

P(E1) = .05, P(E2) = .20, P(E3) = .20, P(E4) = .25, P(E5) = .15, P(E6) = .10, and P(E7) = .05

Let:

A{E1,E4,E6}

B{E2,E4,E7}

C{E2,E3,E5,E7}

P(A) = 0.05 + 0.25 + 0.10 = 0.40

P(B) = 0.20 + 0.25 + 0.05 = 0.50

P(C) = 0.20 + 0.20 + 0.15 + 0.05 = 0.60

AUB = {E1, E2, E4, E6, E7}

P(A u B) = 0.05 + 0.20 + 0.25 + 0.10 + 0.05 = 0.65

AnB = {E4}

P(A n B) = 0.25

A and C are mutually exclusive if AnC = ∅

A n C = ∅

Hence, A and C are mutually exclusive.

B complement = B' = {E1, E3, E5, E6}

P(B') = 0.05 + 0.20 + 0.15 + 0.10 = 0.5

7. d. 64

8. i. 32

9. c. 125

10. j. none of the above

11. d. 81

12. i. 216

13. e. none of the above

14. g. 240

15. e. none of the above

16. g. 32

17.   e. none of the above

answer: 4  

the square root of 16 is 4. it is a very simple mathematic concept. a square root when a number multiplied by itself will result in a number. here, the number 16 comes when 4 is multiplied by 4. hence the square root of 16 is 4. you can always figure out a square root by the inverse operation of squaring.