The probability that certain electronic component fails when first...

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

Options

A $0.9$
B $0.01$
C $0.119$
D $0.891$

Correct answer

D. $0.891$

Step-by-step solution

P

(The electronic component fails when first

\begin{aligned} & \text{ used })=P(F)=0.10 \\ & \therefore P(\bar{F})=1-P(F)=0.90 \end{aligned}

Let

E

be the event that a new component will last for one year, then

P(E)=P(F) \cdot P \left(\frac{E}{F}\right)+P(\bar{F}) P \left(\frac{E}{\bar{F}}\right) [Total probability theorem]

=0.10

\times0+0.90 \times0.99=0.891

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