Agroup of students were asked whether they take french class, art class, both classes or neither classes. the table shows the probabilities of the results

art | not art | total
french | 0.2 | 0.4 | 0.6
not french | 0.35| 0.05 | 0.4
total | 0.55 | 0.45 | 1.00

let a represent taking french class and b represent taking art class.

which statement is true?

a. taking art class and taking french class are not independent events because p(a|b)=p(a) and p(b|a)=p(b) .

b. taking art class and taking french class are independent events because p(a|b)=p(a) and p(b|a)=p(b) .

c. taking art class and taking french class are independent events because p(a|b)≠p(a) and p(b|a)≠p(b) .

d. taking art class and taking french class are not independent events because p(a|b)≠p(a) and p(b|a)≠p(b) .< < < < < < <