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Suppose that a shop has an equal number of LED bulbs of two different types. The probability of an LED bulb lasting more than hours given that it is of Type 0.7 is , and given that it is of Type 2 is 0.4. The probability that an LED bulb chosen uniformly at random lasts more than 100 hours is _________.
Correct answer is '0.55'. Can you explain this answer?
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Suppose that a shop has an equal number of LED bulbs of two different ...
Suppose that a shop has an equal number of LED bulbs of two different types. ==> Therefore
Probability of Taking Type 1 Bulb => 0.5
Probability of Taking Type 2 Bulb => 0.5
The probability of an LED bulb lasting more than 100 hours given that it is of Type 1 is 0.7, and given that it is of Type 2 is 0.4.
Prob(100+ | Type1) => 0.7
Prob(100+| Type2) => 0.4
Prob(100+) => Prob(100+ | Type1) * Prob(Type1) + Prob(100+ | Type2) * Prob(Type2)
= 0.7 * .5 + .4 * .5
= 0.55
Probability of Taking Type 1 Bulb => 0.5
Probability of Taking Type 2 Bulb => 0.5
The probability of an LED bulb lasting more than 100 hours given that it is of Type 1 is 0.7, and given that it is of Type 2 is 0.4.
Prob(100+ | Type1) => 0.7
Prob(100+| Type2) => 0.4
Prob(100+) => Prob(100+ | Type1) * Prob(Type1) + Prob(100+ | Type2) * Prob(Type2)
= 0.7 * .5 + .4 * .5
= 0.55
SIMPLY-
TYPE-1 bulbs ===>let total =10 then 7 are going for 100 years
TYPE-2 bulbs====>let total=10 then 4 are going for 100 years
TOTAL==>20 out of which 11 are going for 100 years ..THEREFORE probability=11/20=.55
TYPE-1 bulbs ===>let total =10 then 7 are going for 100 years
TYPE-2 bulbs====>let total=10 then 4 are going for 100 years
TOTAL==>20 out of which 11 are going for 100 years ..THEREFORE probability=11/20=.55
Most Upvoted Answer
Suppose that a shop has an equal number of LED bulbs of two different ...
The given problem involves finding the probability that an LED bulb chosen randomly from a shop will last more than 100 hours. We are provided with the probabilities of an LED bulb of two different types lasting more than a certain number of hours. Let's solve this problem step by step.
1. Define the problem:
- We want to find the probability that an LED bulb chosen randomly from the shop will last more than 100 hours.
- We are given the probabilities of an LED bulb of Type 0.7 lasting more than a certain number of hours and Type 2 lasting more than a certain number of hours.
2. Determine the probability of an LED bulb lasting more than 100 hours given its type:
- Let P(Type 0.7) be the probability that an LED bulb is of Type 0.7, and P(Type 2) be the probability that an LED bulb is of Type 2.
- Let P(>100 | Type 0.7) be the probability that an LED bulb of Type 0.7 lasts more than 100 hours, and P(>100 | Type 2) be the probability that an LED bulb of Type 2 lasts more than 100 hours.
- We are given that P(>100 | Type 0.7) = 0.7 and P(>100 | Type 2) = 0.4.
3. Apply the law of total probability:
- The law of total probability states that the probability of an event can be found by considering all possible outcomes and their probabilities.
- In this case, we need to consider both types of LED bulbs and their probabilities.
- The probability of an LED bulb lasting more than 100 hours can be calculated as:
P(>100) = P(Type 0.7) * P(>100 | Type 0.7) + P(Type 2) * P(>100 | Type 2)
= 0.5 * 0.7 + 0.5 * 0.4
= 0.35 + 0.2
= 0.55
4. Conclusion:
- The probability that an LED bulb chosen uniformly at random from the shop will last more than 100 hours is 0.55.
- This means that there is a 55% chance that a randomly chosen LED bulb will last more than 100 hours.
In summary, the probability that an LED bulb chosen randomly from the shop will last more than 100 hours is 0.55. This result is obtained by applying the law of total probability and considering the probabilities of the two types of LED bulbs lasting more than 100 hours.
1. Define the problem:
- We want to find the probability that an LED bulb chosen randomly from the shop will last more than 100 hours.
- We are given the probabilities of an LED bulb of Type 0.7 lasting more than a certain number of hours and Type 2 lasting more than a certain number of hours.
2. Determine the probability of an LED bulb lasting more than 100 hours given its type:
- Let P(Type 0.7) be the probability that an LED bulb is of Type 0.7, and P(Type 2) be the probability that an LED bulb is of Type 2.
- Let P(>100 | Type 0.7) be the probability that an LED bulb of Type 0.7 lasts more than 100 hours, and P(>100 | Type 2) be the probability that an LED bulb of Type 2 lasts more than 100 hours.
- We are given that P(>100 | Type 0.7) = 0.7 and P(>100 | Type 2) = 0.4.
3. Apply the law of total probability:
- The law of total probability states that the probability of an event can be found by considering all possible outcomes and their probabilities.
- In this case, we need to consider both types of LED bulbs and their probabilities.
- The probability of an LED bulb lasting more than 100 hours can be calculated as:
P(>100) = P(Type 0.7) * P(>100 | Type 0.7) + P(Type 2) * P(>100 | Type 2)
= 0.5 * 0.7 + 0.5 * 0.4
= 0.35 + 0.2
= 0.55
4. Conclusion:
- The probability that an LED bulb chosen uniformly at random from the shop will last more than 100 hours is 0.55.
- This means that there is a 55% chance that a randomly chosen LED bulb will last more than 100 hours.
In summary, the probability that an LED bulb chosen randomly from the shop will last more than 100 hours is 0.55. This result is obtained by applying the law of total probability and considering the probabilities of the two types of LED bulbs lasting more than 100 hours.
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Suppose that a shop has an equal number of LED bulbs of two different types. The probability of an LED bulb lasting more than hours given that it is of Type 0.7 is , and given that it is of Type 2 is 0.4. The probability that an LED bulb chosen uniformly at random lasts more than 100 hours is _________.Correct answer is '0.55'. Can you explain this answer?
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Suppose that a shop has an equal number of LED bulbs of two different types. The probability of an LED bulb lasting more than hours given that it is of Type 0.7 is , and given that it is of Type 2 is 0.4. The probability that an LED bulb chosen uniformly at random lasts more than 100 hours is _________.Correct answer is '0.55'. Can you explain this answer? for Computer Science Engineering (CSE) 2024 is part of Computer Science Engineering (CSE) preparation. The Question and answers have been prepared according to the Computer Science Engineering (CSE) exam syllabus. Information about Suppose that a shop has an equal number of LED bulbs of two different types. The probability of an LED bulb lasting more than hours given that it is of Type 0.7 is , and given that it is of Type 2 is 0.4. The probability that an LED bulb chosen uniformly at random lasts more than 100 hours is _________.Correct answer is '0.55'. Can you explain this answer? covers all topics & solutions for Computer Science Engineering (CSE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Suppose that a shop has an equal number of LED bulbs of two different types. The probability of an LED bulb lasting more than hours given that it is of Type 0.7 is , and given that it is of Type 2 is 0.4. The probability that an LED bulb chosen uniformly at random lasts more than 100 hours is _________.Correct answer is '0.55'. Can you explain this answer?.
Suppose that a shop has an equal number of LED bulbs of two different types. The probability of an LED bulb lasting more than hours given that it is of Type 0.7 is , and given that it is of Type 2 is 0.4. The probability that an LED bulb chosen uniformly at random lasts more than 100 hours is _________.Correct answer is '0.55'. Can you explain this answer? for Computer Science Engineering (CSE) 2024 is part of Computer Science Engineering (CSE) preparation. The Question and answers have been prepared according to the Computer Science Engineering (CSE) exam syllabus. Information about Suppose that a shop has an equal number of LED bulbs of two different types. The probability of an LED bulb lasting more than hours given that it is of Type 0.7 is , and given that it is of Type 2 is 0.4. The probability that an LED bulb chosen uniformly at random lasts more than 100 hours is _________.Correct answer is '0.55'. Can you explain this answer? covers all topics & solutions for Computer Science Engineering (CSE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Suppose that a shop has an equal number of LED bulbs of two different types. The probability of an LED bulb lasting more than hours given that it is of Type 0.7 is , and given that it is of Type 2 is 0.4. The probability that an LED bulb chosen uniformly at random lasts more than 100 hours is _________.Correct answer is '0.55'. Can you explain this answer?.
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