You are given a free play at the following lottery game: Three balls are drawn at random from among 11 balls numbered 1 through 11. Players win the following prize amounts for guessing which balls are drawn: • $212 for correctly guessing all three numbers. • $28 for correctly guessing exactly two of the three numbers. $13 for correcting guessing exactly one of the three numbers. Additionally, if the player guesses all three numbers in the order that they are drawn, the player wins another $1,016 (on top of the $212 won for guessing all three number). What is the expected (average) amount won playing this game? Hint: If you ignore the extra amount won by guessing the numbers in the correct order, then this is precisely the problem we did in class with a different number of balls and dollar amounts and you can (and should) compute the expected amount won in the same way. Then compute the expected amount of bonus money won as if it were a different game (where it matters what order the balls are drawn). Apply linearity of expectation. Input your answer in dollars, rounding to the nearest cent. For example, e≈ 2.718281828 and so $e would round to $2.72.
You are given a free play at the following lottery game: Three balls are drawn at random from among 11 balls numbered 1 through 11. Players win the following prize amounts for guessing which balls are drawn: • $212 for correctly guessing all three numbers. • $28 for correctly guessing exactly two of the three numbers. $13 for correcting guessing exactly one of the three numbers. Additionally, if the player guesses all three numbers in the order that they are drawn, the player wins another $1,016 (on top of the $212 won for guessing all three number). What is the expected (average) amount won playing this game? Hint: If you ignore the extra amount won by guessing the numbers in the correct order, then this is precisely the problem we did in class with a different number of balls and dollar amounts and you can (and should) compute the expected amount won in the same way. Then compute the expected amount of bonus money won as if it were a different game (where it matters what order the balls are drawn). Apply linearity of expectation. Input your answer in dollars, rounding to the nearest cent. For example, e≈ 2.718281828 and so $e would round to $2.72.
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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Transcribed Image Text:You are given a free play at the following lottery game: Three balls
are drawn at random from among 11 balls numbered 1 through 11.
Players win the following prize amounts for guessing which balls are
drawn:
• $212 for correctly guessing all three numbers.
• $28 for correctly guessing exactly two of the three numbers.
$13 for correcting guessing exactly one of the three numbers.
Additionally, if the player guesses all three numbers in the order that
they are drawn, the player wins another $1,016 (on top of the $212
won for guessing all three number).
What is the expected (average) amount won playing this game?
Hint: If you ignore the extra amount won by guessing the numbers in
the correct order, then this is precisely the problem we did in class
with a different number of balls and dollar amounts and you can (and
should) compute the expected amount won in the same way. Then
compute the expected amount of bonus money won as if it were a
different game (where it matters what order the balls are drawn).
Apply linearity of expectation.
Input your answer in dollars, rounding to the nearest cent. For
example, e≈ 2.718281828 and so $e would round to $2.72.
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