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BITSAT2020MathematicsProbabilityActual

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

  1. A0.99
  2. B0.871
  3. C0.891
  4. D0.762

Correct answer

C. 0.891

Step-by-step solution

Probability that the electronic component fails when first used is P(F)=0.10 . Therefore, P (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) P ( E F )+P (F^ ) P ( E F^ ) [total probability theorem] =0.10 0+0.90 0.99=0.891

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