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BITSAT 2020
Exam
BITSAT
Year
2020
Subject
Mathematics
Chapter
Probability

BITSAT 2020 · Mathematics · Probability

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 0.99.0.99. 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)=0.10P(F)=0.10. Therefore, P(F′)=1−P(F)=0.90P\left(F^{\prime}\right)=1-P(F)=0.90 Let EE be the event that a new component will last for one year.  Then, P(E)=P(F)P(EF)+\text{ Then, } P(E)=P(F) P \left(\frac{E}{F}\right)+ P \left(F^{\prime}\right)P\left(\frac{E}{F^{\prime}}\right) [totalprobabilitytheorem]total probability theorem]=0.10 \times0+0.90 \times0.99=0.891
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