{"status": "success", "data": {"description_md": "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 has been rolled, then the player wins $1$ dollar. If the number chosen appears on the bottom of both of the dice, then the player wins $2$ dollars. If the number chosen does not appear on the bottom of either of the dice, the player loses $1$ dollar. What is the expected return to the player, in dollars, for one roll of the dice?\n\n$\\textbf{(A) } -\\frac{1}{8} \\qquad\\textbf{(B) } -\\frac{1}{16} \\qquad\\textbf{(C) } 0 \\qquad\\textbf{(D) } \\frac{1}{16} \\qquad\\textbf{(E) } \\frac{1}{8}$", "description_html": "

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 has been rolled, then the player wins 1 dollar. If the number chosen appears on the bottom of both of the dice, then the player wins 2 dollars. If the number chosen does not appear on the bottom of either of the dice, the player loses 1 dollar. What is the expected return to the player, in dollars, for one roll of the dice?

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\\textbf{(A) } -\\frac{1}{8} \\qquad\\textbf{(B) } -\\frac{1}{16} \\qquad\\textbf{(C) } 0 \\qquad\\textbf{(D) } \\frac{1}{16} \\qquad\\textbf{(E) } \\frac{1}{8}

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Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.

", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 4, "problem_name": "2007 AMC 10B Problem 22", "can_next": true, "can_prev": true, "nxt": "/problem/07_amc10B_p23", "prev": "/problem/07_amc10B_p21"}}