Mathematics - Probability Question with Solution | TestHub

MathematicsProbabilityTotal probability/Bay's TheoremMedium2 minPYQ_2024

MathematicsMediumsingle choice

The probability that certain electronic component fails when first used is 0.10 . If it does not fail immediately, the probability that it lasts for one year is 0.99 . The probability that a new component will last for one year is

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Answer:

Solution:

$P$ (The electronic component fails when first $used) = P (F) = 0.10 ∴ P (\overset{ˉ}{F}) = 1 - P (F) = 0.90$ Let $E$ be the event that a new component will last for one year, then $P (E) = P (F) \cdot P (\frac{E}{F}) + P (\overset{ˉ}{F}) P (\frac{E}{F ˉ})$ [Total probability theorem] $= 0.10 \times 0 + 0.90 \times 0.99 = 0.891$

Stream:BITSATSubject:MathematicsTopic:ProbabilitySubtopic:Total probability/Bay's Theorem

⏱ 2mℹ️ Source: PYQ_2024

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