Q64 / 100 · BITSAT 2024 (Memory Based Paper 2) · Mathematics

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

  • A
    $0.9$
  • B
    $0.01$
  • C
    $0.119$
  • Correct answer
    D
    $0.891$

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] $=0.10 \times 0+0.90 \times 0.99=0.891$

Hence, the correct answer is option: 'D'.

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