Abortion. The following table from Daniel (1995) shows the results from a questi

Question

Abortion. The following table from Daniel (1995) shows the results from a questionnaire about free abortion. The survey was conducted in an American city and comprised 500 individuals partitioned 2 according to the area of the city where they lived (A, B, C or D) 10.1 "How do vou feel about free abortion?" 100 115 50 35 Total300 Area For (F) Against (I) Undecided (U) Total 125 125 125 125 500 20 60 50 135 15 40 65 1. Estimate the probability that a random individual from the sample of 500 was for free abortion. was against free abortion. was undecided. lived in area B was for free abortion given that he/she lived in area B was undecided or lived in area D 2. Estimate the following probabilities PAn U) PIU D PD)

Explanation / Answer

Solution:

(All probabilities are calculated by using given table.)

Question 1

Probability that a random individual from the sample was for free abortion = P(F) = 300/500 = 0.60

Probability that a random individual from the sample was against free abortion = P(I) = 135/500 = 0.27

Probability that a random individual from the sample was undecided = P(U) = 65/500 = 0.13

Probability that a random individual lived in area B = P(B) = 125/500 = 0.25

Probability that a random individual was for free abortion given that he/she lived in area B = P(F/B) =

P(F/B) = 115/125 = 0.92

Probability that a random individual was undecided or lived in area D = P(U or D)

P(U or D) = P(U) + P(D) – P(U and D)

P(U) = 65/500 = 0.13

P(D) = 125/500 = 0.25

P(U and D) = 40/500 = 0.08

P(U or D) = 0.13+ 0.25 – 0.08 = 0.30

Probability that a random individual was undecided or lived in area D = 0.30

Question 2

P(A U) = 5/500 = 0.01

P(I D) = P(I) + P(D) – P(I D) = (135/500) + (125/500) – (50/500) = 0.27 + 0.25 – 0.10 = 0.42

P(I D) = 0.42

P(Dc) = 1 – P(D) = 1 – 125/500 = 1 – 0.25 = 0.75

P(I/D) = 50/125 = 0.40

P(B/U) = 5/65 = 0.076923

P(F) = 300/500 = 0.60

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