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Th e probability th at certain electr on ic 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
  • c)
    0.891
  • d)
    0.762
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
Th e probability th at certain electr on ic component fails when first...
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.
[total probability theorem]
= 0.10 × 0 + 0.90 × 0.99 = 0.891.
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Most Upvoted Answer
Th e probability th at certain electr on ic component fails when first...
Probability of a Component Failure

Given:
- Probability of a component failing when first used = 0.10
- Probability of a component lasting for one year if it does not fail immediately = 0.99

To find:
- Probability that a new component will last for one year



Solution:

Case 1: Component Fails When First Used

The probability of a component failing when first used is 0.10. Therefore, the probability of a new component not failing when first used is:

P(Component does not fail when first used) = 1 - P(Component fails when first used)
P(Component does not fail when first used) = 1 - 0.10
P(Component does not fail when first used) = 0.90

Case 2: Component Does Not Fail When First Used

If the component does not fail when first used, then the probability of it lasting for one year is 0.99. Therefore, the probability of a new component lasting for one year is:

P(Component lasts for one year) = P(Component does not fail when first used) * P(Component lasts for one year if it does not fail immediately)
P(Component lasts for one year) = 0.90 * 0.99
P(Component lasts for one year) = 0.891

Therefore, the probability that a new component will last for one year is 0.891, which is option (c).
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Th e probability th at certain electr on ic 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 isa)0.99b)0.871c)0.891d)0.762Correct answer is option 'C'. Can you explain this answer?
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Th e probability th at certain electr on ic 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 isa)0.99b)0.871c)0.891d)0.762Correct answer is option 'C'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Th e probability th at certain electr on ic 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 isa)0.99b)0.871c)0.891d)0.762Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Th e probability th at certain electr on ic 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 isa)0.99b)0.871c)0.891d)0.762Correct answer is option 'C'. Can you explain this answer?.
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