roblem #2. The table below shows (some of) the results of a study on i00 adults

Question

roblem #2. The table below shows (some of) the results of a study on i00 adults in which researchers examined the association between the occurrence of a mutation of the A gene and disease X. A mutation no A mutation tota has X does not have X total 12 132 982 1600 a) (1 point) Fill in the missing cells in the table above. Let A be the event that a randomly selected person out of the 1000 participants in the study has the mutation of the A gene. Let X be the event that a randomly selected person out of the 1000 participants in the study has disease X. b) (1 point) Compute P(x). PLX)- 818 c) (1 point) Compute P(A). 4 128 d) (1 point) Compute P(X and A). e) (I point) Compute P(AIX). loae f) (1 point) Compute P(XA). 3 8) (3 points) Explain in the context of the study what P(A|X) means.ooo Proboloility thut op X b) (8 points) Explain in the context of the study what P(X |A) means. Robabity thot o

Explanation / Answer

(b)P(X)=18/1000=0.018

(c)P(A)=138/1000=0.138

(d)P(X and A)=6/1000=0.006

(e)P(A/X)=P(A and X)/P(X)=(6/1000)/(18/1000)=1/3=0.33333

(f)P(X/A)=P(X and A)/P(A)=(6/1000)/(138/1000)=1/23

(g)P(A/X) is the probability that randomly selected person will have mutation of A gene given that person has disease.

(h)P(X/A) is the probability that randomly selected person will have disease given that person have mutation of A gene.

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