Solutions HWB6

3.22: Make a tree diagram with first branching for the market conditions MG (market growth), MS (market stagnation), MR (market recession)

and the second branching for the prediction PG (predict growth), PS (predict stagnation), PR (predict recession).

EVENT PROBABILITY

PG MG&PG (.20)(.80) = .16

MG PS MG&PS (.20)(.10) = .02

PR MG&PR (.20)(.10) = .02

PG MS&PG (.70)(.10) = .07

MS PS MS&PS (.70)(.80) = .56

PR MS&PR (.70)(.10) = .07

PG MR&PG (.10)(.10) = .01

MR PS MR&PS (.10)(.10) = .01

PR MR&PR (.10)(.80) = .08

Pr(PG) = .16 + .07 + .01 = .24

Pr(PS) = .02 + .56 + .01 = .59

Pr(PR) = .02 + .07 + .08 = .17

3.22a: Pr(MG | PG) = Pr(MG&PG)/Pr(PG) = (.16)/(.24)= 16/24 = 2/3

3.22b: Pr(MS | PG) = Pr(MS&PG)/Pr(PG) = (.07)/(.24)= 7/24

3.22c: Pr(MR | PG) = Pr(MR&PG)/Pr(PG) = (.01)/(.24)= 1/24

3.40: You can use the formulas as shown in parts 3.40a, 3.40b, 3.40c, and 3.40d below.

Or you can use a Venn diagram such as the one of Figure 3.1 on page 86.

The parts of the Venn diagram are labeled as follows:

E1 = “Read daily newspaper”. Pr(E1) = .60

E2 = “Read weekly news magazine”. Pr(E2) = .40

II = “Read both”. Pr(Read both) = Pr(E1)Pr(E2 | E1) = (.60)(.50) = .30

I = “Read daily newspaper but not weekly news magazine” = E1&Not E2 Pr(I) = Pr(E1) – Pr(II) = .60 –.30 = .30

III = “Read weekly news magazine but not daily newspaper” = E2&Not E1 Pr(III) = Pr(E2) – Pr(II) = .40 –.30 = .10

IV = “Read neither” = S - I U II U III Pr(IV) = 1 – Pr(I U II U III) = 1 - .70 = .30

3.40a: Pr(Read both) = Pr(E1)Pr(E2 | E1) = (.60)(.50) = .30

3.40b: Pr(At least one) = Pr(E1) + Pr(E2) – Pr(Read both) = .60 + .40 - .30 = .70

3.40c: Pr(Read neither) = 1 – Pr(Read both) = 1 - .70 = .30

3.40d: Pr(Read daily newspaper | Read weekly news magazine) = Pr(Read both)/Pr(Read weekly news magazine) = (.30)/(.40) = .75