{"status": "success", "data": {"description_md": "A bag contains two red beads and two green beads. You reach into the bag and pull out a bead, replacing it with a red bead regardless of the color you pulled out. What is the probability that all beads in the bag are red after three such replacements?\n\n$\\textbf{(A) } \\frac{1}{8} \\qquad\\textbf{(B) } \\frac{5}{32} \\qquad\\textbf{(C) } \\frac{9}{32} \\qquad\\textbf{(D) } \\frac{3}{8} \\qquad\\textbf{(E) } \\frac{7}{16}$", "description_html": "<p>A bag contains two red beads and two green beads. You reach into the bag and pull out a bead, replacing it with a red bead regardless of the color you pulled out. What is the probability that all beads in the bag are red after three such replacements?</p>\n<p> <span class=\"katex--inline\">\\textbf{(A) } \\frac{1}{8} \\qquad\\textbf{(B) } \\frac{5}{32} \\qquad\\textbf{(C) } \\frac{9}{32} \\qquad\\textbf{(D) } \\frac{3}{8} \\qquad\\textbf{(E) } \\frac{7}{16}</span> </p>\n<hr><p>Full credit goes to <a href=\"https://maa.org/\">MAA</a> for authoring these problems. These problems were taken on the <a href=\"https://artofproblemsolving.com/\">AOPS</a> website.</p>", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 4, "problem_name": "2003 AMC 10B Problem 21", "can_next": true, "can_prev": true, "nxt": "/problem/03_amc10B_p22", "prev": "/problem/03_amc10B_p20"}}