Kayla has a bag of M&Ms. Her bag has red, blue, yellow, brown, green, and orange M&Ms. If she picks a candy without looking:

- The probability of picking a red M&M is one fourth.
- Red and orange have an equal probability of being picked.
- The probability of picking a brown M&M is half the probability of picking a red M&M.
- Brown and yellow have an equal probability of being picked.
- Blue and green have an equal probability of being picked.

If Kayla had 24 M&Ms, how many would be:

- Yellow? _______
- Brown? _______
- Green? _______

Red M&M probability:$\frac{1}{4}\backslash frac\{1\}\{4\}$.Orange M&M probability:Since orange and red have equal probabilities, the probability of picking an orange M&M is also $\frac{1}{4}\backslash frac\{1\}\{4\}$.Brown M&M probability:The probability of picking a brown M&M is half the probability of picking a red M&M, so:$Probabilityofbrown=\frac{1}{4}\times \frac{1}{2}=\frac{1}{8}\backslash text\{Probability\; of\; brown\}\; =\; \backslash frac\{1\}\{4\}\; \backslash times\; \backslash frac\{1\}\{2\}\; =\; \backslash frac\{1\}\{8\}$

Yellow M&M probability:Brown and yellow have equal probabilities, so the probability of picking a yellow M&M is also $\frac{1}{8}\backslash frac\{1\}\{8\}$.Blue and Green M&M probability:Blue and green have equal probabilities, and the remaining probability must be split between them.Total probability accounted for:

$\frac{1}{4}+\frac{1}{4}+\frac{1}{8}+\frac{1}{8}=\frac{2}{4}+\frac{2}{8}=\frac{1}{2}+\frac{1}{4}=\frac{3}{4}\backslash frac\{1\}\{4\}\; +\; \backslash frac\{1\}\{4\}\; +\; \backslash frac\{1\}\{8\}\; +\; \backslash frac\{1\}\{8\}\; =\; \backslash frac\{2\}\{4\}\; +\; \backslash frac\{2\}\{8\}\; =\; \backslash frac\{1\}\{2\}\; +\; \backslash frac\{1\}\{4\}\; =\; \backslash frac\{3\}\{4\}$Remaining probability for blue and green:

$1-\frac{3}{4}=\frac{1}{4}1\; \u2013\; \backslash frac\{3\}\{4\}\; =\; \backslash frac\{1\}\{4\}$So each of blue and green has a probability of $\frac{1}{8}\backslash frac\{1\}\{8\}$.

Calculations for 24 M&Ms:Yellow M&Ms:$24\times \frac{1}{8}=324\; \backslash times\; \backslash frac\{1\}\{8\}\; =\; 3$Brown M&Ms:$24\times \frac{1}{8}=324\; \backslash times\; \backslash frac\{1\}\{8\}\; =\; 3$Green M&Ms:$24\times \frac{1}{8}=324\; \backslash times\; \backslash frac\{1\}\{8\}\; =\; 3$Answers: