In a survey conducted in the State of Arkansas high schools to study the correlation between senior year scores in mathematics and enrollment in engineering colleges, 400 out of 1000 surveyed seniors have studied mathematics. Engineering enrollment shows that, of the 1000 seniors, 150 students have studied mathematics and 29 have not. Determine the probabilities of the following events:

(a) A student neither studied mathematics nor enrolled in engineering.

(b) A student who studied math is enrolled in engineering.

(c) A student enrolled in engineering did not study math.