A student enrolled in a degree program takes a total of thirty-two courses, indexed by i= 1,...,32 in order of appearance on the transcript, and also spread evenly over eight semesters. Each course is graded on an Athrough Dscale, and the events A_i, B_i, C_iand D_idenote that the student earned the respective grade when taking the i^thcourse. (Each course is attempted once only.)

(i)Consider the four events A₁, B₁, C₂and D₂. Determine whether each possible pair has empty or nonempty intersection, and draw the four events on a Venn diagram.

(ii) Express the event

E = " GPA for the first semester equals 3.75 "

symbolically in terms of A_i's, B_i's, C_i's and D_i's (as appropriate).

(iii) Express the event

F = " no D's are earned in the first two semesters"

symbolically using D_i's.

(iv) Express the event