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There are three person aged 60 65 and 70 years old thermal probability for these three person for another 5 year are 0.70 4.4 and 0.2 respectively what is the probability that at least two of them would survive another 5 year?
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There are three person aged 60 65 and 70 years old thermal probability...
Problem Statement:
There are three persons aged 60, 65, and 70 years old. The thermal probability for these three persons for another 5 years are 0.70, 0.44, and 0.20, respectively. What is the probability that at least two of them would survive another 5 years?
Solution:
Let's define the events:
- S1: Person aged 60 years old survives another 5 years
- S2: Person aged 65 years old survives another 5 years
- S3: Person aged 70 years old survives another 5 years
Using the given thermal probabilities, we can find the probability of each event as follows:
- P(S1) = 0.70
- P(S2) = 0.44
- P(S3) = 0.20
Now, we need to find the probability that at least two of them would survive another 5 years. We can calculate this probability by finding the sum of the probabilities of the following three cases:
- Case 1: Persons 1 and 2 survive and person 3 does not survive
- Case 2: Persons 1 and 3 survive and person 2 does not survive
- Case 3: Persons 2 and 3 survive and person 1 does not survive
Let's calculate the probability of each case:
- Case 1: P(S1 ∩ S2 ∩ S3') = P(S1) x P(S2) x (1 - P(S3)) = 0.70 x 0.44 x 0.80 = 0.2464
- Case 2: P(S1 ∩ S3 ∩ S2') = P(S1) x P(S3) x (1 - P(S2)) = 0.70 x 0.20 x 0.56 = 0.0784
- Case 3: P(S2 ∩ S3 ∩ S1') = P(S2) x P(S3) x (1 - P(S1)) = 0.44 x 0.20 x 0.30 = 0.0264
Finally, we can find the probability that at least two of them would survive another 5 years by adding
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There are three person aged 60 65 and 70 years old thermal probability for these three person for another 5 year are 0.70 4.4 and 0.2 respectively what is the probability that at least two of them would survive another 5 year?
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There are three person aged 60 65 and 70 years old thermal probability for these three person for another 5 year are 0.70 4.4 and 0.2 respectively what is the probability that at least two of them would survive another 5 year? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about There are three person aged 60 65 and 70 years old thermal probability for these three person for another 5 year are 0.70 4.4 and 0.2 respectively what is the probability that at least two of them would survive another 5 year? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for There are three person aged 60 65 and 70 years old thermal probability for these three person for another 5 year are 0.70 4.4 and 0.2 respectively what is the probability that at least two of them would survive another 5 year?.
There are three person aged 60 65 and 70 years old thermal probability for these three person for another 5 year are 0.70 4.4 and 0.2 respectively what is the probability that at least two of them would survive another 5 year? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about There are three person aged 60 65 and 70 years old thermal probability for these three person for another 5 year are 0.70 4.4 and 0.2 respectively what is the probability that at least two of them would survive another 5 year? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for There are three person aged 60 65 and 70 years old thermal probability for these three person for another 5 year are 0.70 4.4 and 0.2 respectively what is the probability that at least two of them would survive another 5 year?.
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