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A bowl contains 12 green candies, 4 yellow candies, and some red candies. The probability of choosing a green candy at random is twice as great as the probability of choosing a red candy at random. What is the probability of choosing a yellow candy at random? E. (2)/(11) F. (2)/(9) G. (1)/(4) H. (3)/(11)

A bowl contains 1212 green candies, 44 yellow candies, and some red candies. The probability of choosing a green candy at random is twice as great as the probability of choosing a red candy at random. What is the probability of choosing a yellow candy at random?\newlineE. (2)/(11)(2)/(11)\newlineF. (2)/(9)(2)/(9)\newlineG. (1)/(4)(1)/(4)\newlineH. (3)/(11)(3)/(11)

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Q. A bowl contains 1212 green candies, 44 yellow candies, and some red candies. The probability of choosing a green candy at random is twice as great as the probability of choosing a red candy at random. What is the probability of choosing a yellow candy at random?\newlineE. (2)/(11)(2)/(11)\newlineF. (2)/(9)(2)/(9)\newlineG. (1)/(4)(1)/(4)\newlineH. (3)/(11)(3)/(11)
  1. Identify Red Candies: Let's find out how many red candies there are. We know the probability of picking a green candy is twice that of picking a red candy. Let's denote the number of red candies as rr. The total number of candies is 1212 (green) + 44 (yellow) + rr (red) = 16+r16 + r.
  2. Calculate Probability Equation: The probability of picking a green candy is 1216+r\frac{12}{16 + r}, and the probability of picking a red candy is r16+r\frac{r}{16 + r}. Since the probability of picking a green candy is twice that of a red candy, we have:\newline1216+r=2×(r16+r)\frac{12}{16 + r} = 2 \times \left(\frac{r}{16 + r}\right).
  3. Solve for Number of Red Candies: Solving the equation: \newline1216+r=2r16+r\frac{12}{16 + r} = \frac{2r}{16 + r},\newline12=2r12 = 2r,\newliner=6r = 6.
  4. Calculate Total Number of Candies: Now, we know there are 66 red candies. The total number of candies is 12+4+6=2212 + 4 + 6 = 22.
  5. Calculate Probability of Yellow Candy: The probability of picking a yellow candy is the number of yellow candies divided by the total number of candies, which is 422\frac{4}{22}. Simplifying this gives:\newline422=211\frac{4}{22} = \frac{2}{11}.

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