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3 June, 13:37

A fire company keeps two rescue vehicles. Because of the demand on the vehicles and the chance of mechanical failure, the probability that a specific vehicle is available when needed is 90%. The availability of one vehicle is independent of the availability of the other. Find the probability that neither vehicle is available at a given time?

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  1. 3 June, 13:42
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    The probability that neither vehicle is available at a given time is 0.01

    Step-by-step explanation:

    Let us assume the two needed vehicles are A and Q.

    Let P (A) be the probability of the vehicle A available when needed.

    And, P (Q) be the probability of the vehicle Q available when needed.

    Now, P (A) = 90 % = 0.90

    ⇒ P (not A) = 1 - P (A)

    = 1 - 0.9 = 0.1

    ⇒ P (not A) = 0.1

    Similarly, P (Q) = 90 % = 0.90

    ⇒ P (not Q) = 1 - P (Q)

    = 1 - 0.9 = 0.1

    ⇒ P (not Q) = 0.1

    So, the probability that both the vehicles are NOT available when needed

    = P (not A) x P (not Q)

    = 0.1 x 0.1 = 0.01

    Hence, the probability that neither vehicle is available at a given time is 0.01
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