3 men aged 50years, 60years, 70years. Probability to live 5years more is 0.9 for 50years old, 0.7 for 60years old and 0.5 for 70years old. Find the probability that exactly two of them remain alive 5years hence.
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Answer:
0.8
Step-by-step explanation:
probability of 50years man to remain alive for 5 years more is P(A1)= 0.9
probability of 50years man to remain not alive is P(A2)= 1-0.9= 0.1
probability of 60years man to remain alive for 5 years more is P(B1)= 0.7
probability of 60years man to remain not alive is P(B2)= 1-0.7= 0.3
probability of 70years man to remain alive for 5 years more is P(C1)= 0.5
probability of 70years man to remain not alive is p(C2)= 1-0.5=0.5
probability of exactly two of them remain alive is
as fallows,
50, 60 are alive+ 60, 70 are alive + 50,70 are alive + three of them are alive
(0.9*0.7*0.5)+(0.7*0.5*0.1)+(0.9*0.5*0.3)
+(0.9*0.7*0.5)
=0.8
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