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 4 out of every 5 red m & ms are followed by a blue one , while one out of every 6 blue m & ms is followed by a red one . what proportion of the m & ms are red ?	Choose the correct choice from the following options:	A) 1 / 29	B) 2 / 29	C) 3 / 29	D) 4 / 29	E) 5 / 29

Rationale: suppose that the fraction of red m & ms is fr and the fraction of blue m & 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 e
Answer: E