From the known data, there is roughly an 85% chance that a person of age 20 years will be
alive at age 75 years. Suppose that 4 people of age 20 years are selected at random. What
is the probability that the number alive at age 75 years will be at least 3?
0.1095
0.8905
0.3685
0.5520
Answers
Step-by-step explanation:
ME know what I should have been looking forward with a block
The answer is the third option, 0.8905
Given
- 85% chance that a person of age 20 years will be alive at the age of 75 years
- 4 people of age 20 years are selected at random.
To Find
the probability that the number alive at age 75 years will be at least 3
Solution
Let A be the event that a person at the age of 20 will live till the age of 75.
P(A) = 85%
= 85/100
= 17/20
Therefore P(not A) = 1 - P(A)
= 1 - 17/20
= 3/20
The probability that at least 3 people are alive till the age of 75 years out of 4 20 years people is
The probability that 3 out of 4 of them is alive + the Probability that all 4 of them are alive
The probability that 3 out of 4 of them are alive
= ⁴C₃ X P(A) X P(A) X P(A) X P(not A)
= 4!/3! X17/20 X 17/20 X 17/20 X 3/20
= 58956/160000
the Probability that all 4 of them are alive
= ⁴C₄ X P(A) X P(A) X P(A) X P(A)
= ⁴C₄ X 17/20 X 17/20 X 17/20 X 17/20
= 83,521/160000
Therefore,
The probability that at least 3 people are alive till the age of 75 years out of 4 20 years people
= 58956/160000 + 83,521/160000
= 142477/160000
= 0.8905 (approx)
Hence, the answer is the third option, 0.8905
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