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There are three persons aged 60, 65 and 70 years old. The survivals probabilities for these three persons for another 5 years are 0.7, 0.4 and 0.2 respectively. What is the probability that at least two of them would survive another five years?
  • a)
    0.425
  • b)
    0.456
  • c)
    0.392
  • d)
    0.388
Correct answer is option 'D'. Can you explain this answer?
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There are three persons aged 60, 65 and 70 years old. The survivals pr...
Given Information:
Three persons aged 60, 65 and 70 years old.
Survivals probabilities for these three persons for another 5 years are 0.7, 0.4 and 0.2 respectively.

To Find: The probability that at least two of them would survive another five years.

Solution:
Let us denote the probability of survival of the three persons by A, B, and C, respectively.

A = Probability of survival of the person aged 60 years old = 0.7
B = Probability of survival of the person aged 65 years old = 0.4
C = Probability of survival of the person aged 70 years old = 0.2

The probability that at least two of them would survive another five years can be calculated using the following formula:

P(at least two persons would survive another five years) = P(A and B and not C) + P(A and C and not B) + P(B and C and not A) + P(A and B and C)

Here,
P(A and B and not C) = Probability that persons A and B would survive another five years, but not C.
= P(A) x P(B) x (1 - P(C))
= 0.7 x 0.4 x (1 - 0.2)
= 0.224

P(A and C and not B) = Probability that persons A and C would survive another five years, but not B.
= P(A) x P(C) x (1 - P(B))
= 0.7 x 0.2 x (1 - 0.4)
= 0.084

P(B and C and not A) = Probability that persons B and C would survive another five years, but not A.
= P(B) x P(C) x (1 - P(A))
= 0.4 x 0.2 x (1 - 0.7)
= 0.048

P(A and B and C) = Probability that all three persons would survive another five years.
= P(A) x P(B) x P(C)
= 0.7 x 0.4 x 0.2
= 0.056

Therefore, the probability that at least two of them would survive another five years is:

P(at least two persons would survive another five years) = 0.224 + 0.084 + 0.048 + 0.056
= 0.388

Hence, the correct answer is option D.
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There are three persons aged 60, 65 and 70 years old. The survivals pr...
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There are three persons aged 60, 65 and 70 years old. The survivals probabilities for these three persons for another 5 years are 0.7, 0.4 and 0.2 respectively. What is the probability that at least two of them would survive another five years?a)0.425b)0.456c)0.392d)0.388Correct answer is option 'D'. Can you explain this answer?
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