Q61 / 125 · BITSAT 2020 · 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
    0.99
  • B
    0.871
  • Correct answer
    C
    0.891
  • D
    0.762

Solution

Probability that the electronic component fails when first used is $P(F)=0.10$. Therefore, $P\left(F^{\prime}\right)=1-P(F)=0.90$ Let $E$ be the event that a new component will last for one year. $\text { Then, } P(E)=P(F) P\left(\frac{E}{F}\right)+P\left(F^{\prime}\right) P\left(\frac{E}{F^{\prime}}\right)$ [total probability theorem] $=0.10 \times 0+0.90 \times 0.99=0.891$

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

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