Question

QUESTION: If one of the subjects is randomly selected, find the probability of selecting someone who lied or had a polygraph indicative of not lying.

	Did the subject actually lie?
	No (did not lie)	Yes (did lie)
Polygraph test indicated that the subject lied.	15	42
Polygraph test indicated that the subject did not lie.	32	9

Answer 1

solution:

the given contingency table as follows

	did the subject actually lie
	NO	Yes	Total
test indicated that subject lie	15	42	57
test indicated that the subject do not lie	32	9	41
total	47	51	98

let P(A) be the probability that the subject actually lie.

so P(A) = 51 / 98 = 0.5204

let P(B) the probability that poligraph test indicating not lied

so, P(B) = 41 / 98 = 0.4184

P(A and B) = 9 / 98 = 0.0918

P(A or B) = P(A) + P(B) - P(A and B)

P(A or B) = 0.5204 + 0.4184 - 0.0918 = 0.847