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Answer:
0.00075
0.02425
0.94575
Step-by-step explanation:
Let E1 be the event that A dies within next 20 years and E2 be the event that B dies within next 20 years.
Probability that E1 occurs = P(E1) = 0.025
Probability that E2 occurs= P(E2)= 0.030
Since the two events does not depend on each other, E1 and E2 are independent events.
For two independents E1 and E2 , the probability that both E1 and E2 occurs simultaneously is P(E1 ∩ E2) is given by:
P(E1 ∩ E2) = P(E1)*P(E2)
Probability that both A and B dies in next 20 years =
Probability that A will die and B will not die is given by=
P(E1 ∩ E2') = P(E1) - P(E1 ∩ E2) = 0.025 - 0.00075 = 0.02425.
Probability that neither A nor B dies is given by=
P(E1' ∩ E2') = 1 - [ P(E1 ∪ E2) ] = 1 - [ P(E1) + P(E2) - P(E1 ∩ E2) ]
= 1 - [0.025 + 0.030 - 0.00075] = 0.94575