An experiment is planned where an automatic lab would be sent to the surface of Saturn....

An experiment is planned where an automatic lab would be sent to the surface of Saturn. If there was life in Saturn, the probability that the lab detects it and correctly reports the finding is 0.5. If there never was life on Saturn, the probability that the lab will erroneously indicate the presence of life is 0.45. Suppose that a fair assessment of the probability that life was ever present on Saturn is 0.1.

(a) Find the probability that the lab says that there was life on Saturn.

(b) If the lab says that there was life on Saturn, what is the probability that the lab is correct (that is, that indeed there was life in Saturn)?

Expert Solution

P(life was present on saturn) = 0.1

P(life wasn't present) = 1 - 0.1 = 0.9

P(lab detects presence of life | life was present) = 0.5

P(lab detects presence of life | life wasn't present) = 0.45

a) P(lab says that there was life on Saturn) = P(lab detects presence of life | life was present) * P(life was present) + P(lab detects presence of life | life wasn't present) * P(life wasn't present)

= 0.5 * 0.1 + 0.45 * 0.9

= 0.455

b) P(there was life in saturn | lab detects presence of life) = P(lab detects presence of life | life was present) * P(life was present) / P(lab says that there was life on Saturn)

= 0.5 * 0.1 / 0.455

= 0.1099

orchestra answered 1 year ago

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