MathDB

9

Part of 2021 AMC 10 Fall

Problems(2)

unfair die

Source: 2021 AMC 10A #9

11/11/2021
When a certain unfair die is rolled, an even number is 33 times as likely to appear as an odd number. The die is rolled twice. What is the probability that the sum of the numbers rolled is even?
<spanclass=′latex−bold′>(A)</span>38<spanclass=′latex−bold′>(B)</span>49<spanclass=′latex−bold′>(C)</span>59<spanclass=′latex−bold′>(D)</span>916<spanclass=′latex−bold′>(E)</span>58<span class='latex-bold'>(A) </span>\dfrac38\qquad<span class='latex-bold'>(B) </span>\dfrac49\qquad<span class='latex-bold'>(C) </span>\dfrac59\qquad<span class='latex-bold'>(D) </span>\dfrac9{16}\qquad<span class='latex-bold'>(E) </span>\dfrac58
AMCAMC 10AMC 10 A
Magical knights!

Source: 2021 Fall AMC10B P9

11/17/2021
The knights in a certain kingdom come in two colors. 27\frac{2}{7} of them are red, and the rest are blue. Furthermore, 16\frac{1}{6} of the knights are magical, and the fraction of red knights who are magical is 22 times the fraction of blue knights who are magical. What fraction of red knights are magical?
<spanclass=′latex−bold′>(A)</span>29<spanclass=′latex−bold′>(B)</span>313<spanclass=′latex−bold′>(C)</span>727<spanclass=′latex−bold′>(D)</span>27<spanclass=′latex−bold′>(E)</span>13<span class='latex-bold'>(A) </span>\frac{2}{9}\qquad<span class='latex-bold'>(B) </span>\frac{3}{13}\qquad<span class='latex-bold'>(C) </span>\frac{7}{27}\qquad<span class='latex-bold'>(D) </span>\frac{2}{7}\qquad<span class='latex-bold'>(E) </span>\frac{1}{3}
AMCAMC 10AMC 10 B