Let D1 and D2 be the numbers obtained by tossing 2 dice Then

Let D_1 and D_2 be the numbers obtained by tossing 2 dice. Then P(D_1 = D_2) = Suppose Stat 243 students are 60% male, 40% female. Long term, 30% of males will get an \"A\", and 50% of females will an \"A\". What percent of Stat 243 students will get an \"A\"?

Solution

a) P(D₁=D₂) = 6/36. hence correct option is C

b) given n = 243, let M be the event that the student is male and F the student is female.

hence P(M) = 0.6 and P(F) = 0.4

Let E be the event that the student will get an \"A\"

hence P(A/M) = 0.3 and P(A/F) = 0.5

therfore P(A) = P(M)*P(A/M) + P(F)*P(A/F) = (0.6*0.3)+(0.4*0.5) = 0.18 + 0.20 = 0.38

c) P(female/A) = [P(F)*P(A/F)]/P(A) = 0.20/0.38 = 10/19

d) P(male/A) = [P(M)*P(A/M)]/P(A) = 0.18/0.38 = 9/19

e) Probability that no box is empty is given by (1/9)+(1/9)+(1/9) = 3/9