At an M&M factory, two types of M&Ms are produced, red and blue. The M&Ms are transported
individually on a conveyor belt. Anna is watching the conveyor belt, and has determined that
four out of every five red M&Ms are followed by a blue one, while one out of every six blue
M&Ms is followed by a red one. What proportion of the M&Ms are red?  Choose the correct choice from the following:
A) 1/29	B) 2/29	C) 3/29	D) 4/29	E) 5/29
Suppose that the fraction of red M&amp;Ms is fr and the fraction of blue M&amp;Ms   is fb. Then the probability that Anna sees a red one emerge next is fr. This probabil-   ity can also be expressed using conditional probabilities as fr = P(blue)P(red after blue) +   P(red)P(red after red), or fr = fb(1=6) + fr(1=5). Likewise, we find fb = fr(4=5) + fb(5=6).   Solving the system of equations gives fb = 24   29 and fr =5/29   correct answer 5/29
<result>E</result>
At an M&M factory, two types of M&Ms are produced, red and blue. The M&Ms are transported
individually on a conveyor belt. Anna is watching the conveyor belt, and has determined that
four out of every five red M&Ms are followed by a blue one, while one out of every six blue
M&Ms is followed by a red one. What proportion of the M&Ms are red?