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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).

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 First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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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).
Transcribed Image Text: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).
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