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25 December, 13:43

In general, after a group makes a reservation at a restaurant, they do not show up 20% of the time. If a restaurant has 8 reservations for the evening, what is the probability that exactly two do not show up?

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  1. 25 December, 14:50
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    P (more than 2 don't show up) = 0.2031

    Step-by-step explanation:

    Multiplication rule for independent events:

    If two events A and B are independent then the multiplication rule state that:

    P (A and B) = P (A) x P (B)

    Find the probability that more than two do not show up:

    The probability that the reservations at the restaurant do not show up is 0.20 (=20%) and there were 8 reservations.

    P (more than 2 don't show up) = 1 - P (less than or equal to 2 don't show up)

    = 1 - (P (none show up) + P (one don't show up) + P (two don't show up)

    =1 - ((0.8⁸) + ₈ C₁ (0.2¹) x (0.8⁷) + ₈ C₂ (0.2²) x (0.8⁶)

    =1 - (0.1678 + 0.3355+0.2936) = 1-0.7969

    P (more than 2 don't show up) = 0.2031
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