A restaurant has 5 tables that can be reserved. The restaurant manager knows that some people will make a reservation and then won’t show up for dinner. The probability that a party will show up for dinner, if they have a reservation, is 0.8. The probability that a party won’t show up is 0.2. The probability of each party showing up is independent. Even though the restaurant only has 5 tables to reserve, they usually accept at least 6 reservations because they know there may be some cancellations.
If 6 reservations are made, what is the probability that all parties will show up? Can the restaurant take 7 reservations without worrying about overbooking? The restaurant manager doesn’t want a probability greater than 0.5 that more than 5 parties will show up.

Find the probability that all the parties will show up at the restaurant.

Find the probability that more than 5 parties show up if 7 reservations are made.

Determine whether the restaurant can take 7 reservations.

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