Question

Consider the drawing of a probability tree for this data. What are the prior probabilities that would be on the tree and what would they be for?

          WOMEN                      EYE COLOR               CHILDREN

                18                            Brown                                No

                22                            Brown                               Yes

                09                            Blue                                   No

                21                            Blue                                  Yes

                12                            Green                                No

                18                            Green                               Yes

            MEN                            EYE COLOR               CHILDREN

                24                            Brown                                No

                16                            Brown                               Yes

                12                            Blue                                   No

                18                            Blue                                  Yes

                10                            Green                                No

                20                            Green                               Yes

Answer 1

Let W and M denote the event of the person being a Woman and Man respectively. Let Br, Bl, G denote the event that the eye colour is Brown, Blue and Green respectively. Let C and A denote the event that the person selected is a Child and Adult respectively.

Based on the given data, by definition of probability,

Probability of occurrence of an event = No. of favorable cases / Total No. of cases

P(W) = P(M) = 100 /200 = 0.5

P(Br) = (18+22+24+16) / 200 = 80 / 200 = 0.40

P(Bl) = (09+21+12+18) / 200 = 60 / 200 = 0.30

P(G) = (12+18+10+20) / 200 = 60 / 200 = 0.30

P(C) = (22+21+18+ 16+18+20) / 200 = 115 / 200 = 0.575

P(A) = (18 + 9 +12+ 24+12+10) / 200 = 85 / 200 = 0.425

P(WC) = (22 + 21 + 18) / 200 = 61 = 200 = 0.305

P(WA) = (18 + 9 + 12) / 200 = 39 / 200 = 0.195

P(MC) = (16 + 18 + 20) / 200 = 0.27

P(MA) = (24 + 12 + 10) / 200 = 0.23

P(WCBr) = 22 /200 = 0.11

P(WCBl) = 21 / 200 = 0.105

P(WCG) = 18 / 200 = 0.09

P(WABr) = 18 /200 = 0.09

P(WABl) = 09 / 200 = 0.045

P(WAG) = 12 / 200 = 0.06

P(MCBr) = 16 /200 = 0.08

P(MCBl) = 18 / 200 = 0.09

P(MCG) = 20 / 200 = 0.10

P(MABr) = 24 / 200 = 0.12

P(MABl) = 12 / 200 = 0.06

P(MAG) = 10 / 200 = 0.05

Tree Diagram: