The probabilities of a husband and his wife surviving for 20 more years are 0.8 and 0.9 respectively. Find the probability that after 20 years: a. both of them are alive b. at least one of them is alive.
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Let A be the event that a husband will be alive after 20 yrs.Let B be the event that a wife will be alive after 20 yrs.Now, PA = 0.8; PB = 0.9Now, PA = 1-PA = 1 - 0.8 = 0.2Now, PB 1 - PB = 1 - 0.9 = 0.1a.Probability that both of them are alive = PA . PB = 0.8×0.9 = 0.72b.Probability that none of them is alive = PA . PB = 0.2×0.1 = 0.02Probability that at least one of them is alive = 1 - 0.02 = 0.08
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Answer:
0.98
Explanation:
A= probablity of wife surviving after 20 years.
B=probablity of husband surviving after 20 years.
P(A)=0.9 P(B)=0.8 P(A`)=1 - 0.9 P(B`) = 1 - 0.8
a). Both of them are alive i.e A and B are alive
P(A∩B)= P(A).P(B)
= (0.9)(0.8)
=0.72
b). at least one of them is alive i.e either A can be alive or B can be alive
= 1 - P(both are dead)
=1 - P(A`∩B`) # since they are independent P
= 1 - (0.2*0.1) P (A∩B )=P(A)*P(B)
=0.98
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