Question

In: Statistics and Probability

Consider the drawing of a probability tree for this data. What are the prior probabilities that...

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

Expert Solution

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:

orchestra answered 1 year ago

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