Question

9 multiple choice 5 points m&m plain candies come in a variety of colors. according to the m&m/mars department of consumer affairs the average distribution of colors in a bag of 100 candies is 30 brown, 20 yellow, 20 red, 10 orange, 10 green, and 10 blue. suppose you have a bag of m&m candies and you take two candies at random, without replacing the first one. what is the probability or drawing an orange then a red? \\( \frac{1}{5} \\) \\( \frac{2}{99} \\) \\( \frac{1}{50} \\) \\( \frac{19}{1000} \\)

Explanation:

Step1: Find total candies

Total candies = \( 30 + 20 + 20 + 10 + 10 + 10 = 100 \)

Step2: Probability of orange first

Number of orange = 10, so \( P(\text{orange}) = \frac{10}{100} = \frac{1}{10} \)

Step3: Probability of red after orange

After removing one orange, total candies = 99, number of red = 20, so \( P(\text{red}|\text{orange}) = \frac{20}{99} \)

Step4: Multiply probabilities

\( P(\text{orange then red}) = \frac{10}{100} \times \frac{20}{99} = \frac{200}{9900} = \frac{2}{99} \)

Answer:

\(\frac{2}{99}\) (the option with \(\frac{2}{99}\))