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MATH / A player chooses one of the numbers 1 through 4. After the choice has been made,…

Problem

Answer published by the source. Consult the official source to check your work against its answer.

problem

A player chooses one of the numbers 1 through 4. After the choice has been made, two regular four-sided (tetrahedral) dice are rolled, with the sides of the dice numbered 1 through 4. If the number chosen appears on the bottom of exactly one die after it is rolled, then the player wins $1.\$1. If the number chosen appears on the bottom of both of the dice, then the player wins $2.\$2. If the number chosen does not appear on the bottom of either of the dice, the player loses $1.\$1. What is the expected return to the player, in dollars, for one roll of the dice? Give your answer as a fraction.
Plain-text mathematical notation (without MathML)
A player chooses one of the numbers 1 through 4. After the choice has been made, two regular four-sided (tetrahedral) dice are rolled, with the sides of the dice numbered 1 through 4. If the number chosen appears on the bottom of exactly one die after it is rolled, then the player wins $1. If the number chosen appears on the bottom of both of the dice, then the player wins $2. If the number chosen does not appear on the bottom of either of the dice, the player loses $1. What is the expected return to the player, in dollars, for one roll of the dice? Give your answer as a fraction.
Original LaTeX notation
A player chooses one of the numbers 1 through 4. After the choice has been made, two regular four-sided (tetrahedral) dice are rolled, with the sides of the dice numbered 1 through 4. If the number chosen appears on the bottom of exactly one die after it is rolled, then the player wins $\$1.$ If the number chosen appears on the bottom of both of the dice, then the player wins $\$2.$ If the number chosen does not appear on the bottom of either of the dice, the player loses $\$1.$ What is the expected return to the player, in dollars, for one roll of the dice? Give your answer as a fraction.

level

Level 5

type

Counting & Probability

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Source and history

task_id
461c987d-90d9-5893-abbf-a1e2ebc4c7eb
task_key
counting~5fand~5fprobability--test--461c987d-90d9-5893-abbf-a1e2ebc4c7eb
task_revision_id
1
config / split
counting_and_probability / test

Official source

initial import