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A light bulb manufacturer knows that 0.07% of all bulbs manufactured are defective. A testing machine is 98% effective. If a randomly selected light bulb is tested and found to be defective, what is the
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A light bulb manufacturer knows that 0.07% of all bulbs manufactured are defective. A testing machine is 98% effective. If a randomly selected light bulb is tested and found to be defective, what is the probability that it actually is defective?

User Aaru
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P[ actually defective & shown as defective] = 98% of 0.08% = 0.0784%
P[ok & shown as defective] = 2% of 99.92% = 1.9984%

P[actually defective | shown as defective] = 0.0784/(0.0784+1.9984) = 3.775% <-------
User Earizon
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