*1. 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 who studied mathematics is enrolled in engineering. Is not enrolled in engineering.

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

(c) A student is not studying engineering.