18 Individuals with a particular medical condition were classified according to

Question

18 Individuals with a particular medical condition were classified according to the presence (7) or absence (M) of a potential toxin in their blood and the onset of the condition (E: early, M. midrange, L: late). The breakdown according to this classification is shown in the two-way contingency table. T0.012 0.124 0.013 N 0.170 0,638 0.043 One of these individuals is selected at random. Find the probability of each of the following events a. The person experienced early onset of the condition. b. The onset of the condition was either midrange or late, in two ways: (0) by adding numbers in the table, and () using the answer to (a) and the Probability Rule for Complements The toxin is present in the person's blood. d. The person experienced early onset of the condition and the toxin is present in the person's blood e. The person experienced early onset of the condition or the toxin is present in the person's blood, in two ways: (0) by finding the cells in the table that correspond to this event and adding their probabilities, and (il) using the Additive Rule of Probability

Explanation / Answer

C) P(toxin is present) = 0.012 + 0.124 + 0.013 = 0.149

D) P(early onset of condition and toxin is present) = 0.012

E) i) P(early onset of condition or toxin is present) = 0.012+0.124+0.013+0.170 = 0.319

ii) P(early onset of condition or toxin is present) = P(early onset of condition) + P(toxin is present) - P(early onset of condition and toxin is present)

= 0.182 + 0.149 - 0.012

= 0.319

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