The probability that a will die within the next 20 years is 0.025, and that b will die within the next

The probability that a will die within the next 20 years is 0.025, and that b will die within the next 20 years is 0.030. what is the probability that both a and b will die within the next 20 years? that a will die and b will not die? that neither a nor b will die?

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  1. 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 = [tex]0.025\times0.03=0.00075[/tex]

    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

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