Solutions to Final Review

1. a. , then, solution is

b. , and break even is when Revenue = Cost, so solution is

2. a.; b. ; d. e. and solution is

3. x = amount of dollars in tax-free bonds, y = amount in CD’s, z = amount in stocks

then x + y + z = 80000, .075x + .08y + .11z = 7455, z = 2x

4. a. =

b.

5. Can’t do here.

6. Maximixe: z = 40x + 30y, x = # of acres oranges, y = # of acres grapefruits

Subj. To : x + y 48

2x + y 80

x 0, y 0

Max Profit = $1760 @ (32, 16)

7. a. A ∩ B = { 1, 5 }

b. A’ È B = { 0, 1, 2, 5, 6, 8, 9 }

8. a. By addition rule P(A ∩ B) = P(A) + P(B) – P(A È B) = .09

b. P(B|A) = =

c. No, A ∩ B Æ

9. a. P(F È R) = P(F) + P(R) – P(R ∩ F) =

b. P(© first ∩© second) = P(© first) *P(© second | © first) =

10. Can’t show diagram but we want P(Jar 2 | Red marble) =

11. 3!*7! = 30240

12. a. = 792

b.

13. n = 8, p = 1/3, q = 2/3, x = 3: P(x = 3) = .273

14. a.

X	0	1	2
P(X)

X = # of green marbles, probabilities found using combinations.

b. E(X) = SX*P(X) =

15. = 7.1 = 6.01