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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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