Expected Winnings in a Lottery A small lottery sells 1000 tickets numbered 000, 001, ...,999; the tickets cost $10 each. When all the tickets have been sold the draw takes place: this consists of a simple ticket from 000 to 999 being chosen at random. For ticket holders the prize structure is as follows: • Your ticket is drawn - win $5000. • Your ticket has the same first two number as the winning ticket, but the third is different - win $100. • Your ticket has the same first number as the winning ticket, but the second number is different - win $10. • All other cases - win nothing. Let the random variable X represent the winnings from a given ticket. Find E(X).

A group of 8 people, including Betty and Bob, are going to take a group photo. In how many ways can they line up, order counting, if Betty and Bob must stand next to each other?    ___________

Fair Division 2. As part of an inheritance, three children, Abby, Ben and Carla, are dividing four vehicles using Sealed Bids. Their bids (in thousands of dollars) for each item are shown below. In the final allocation, Abby gets which items?  (click none, one, or multiple boxes)   Abby Ben Carla Motorcycle  6 10 8 Car 11 14 13 Tractor 6 3 5 Boat 4 3 5 Motorcycle Car Tractor Boat   In addition, she ______to/from the estate: $______ Give your answer to the last question to the nearest dollar (careful here - the original amounts were in thousands of dollars)

Tarot cards are used for telling fortunes, and in a reading, the arrangement of the cards is as important as the cards themselves. How many different readings are possible if five cards are selected from a set of eight Tarot cards? ______ readings