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) .< < < < < < <

D. Taking Art class and taking French class are not independent events because P(A|B)≠P(A) and P(B|A)≠P(B) .

Step-by-step explanation:

We know that for dependent events A and B , the conditional probability of getting a given that B is given by :-

From the given table, if A represent taking French class and B represent taking Art class.

Then P(A)=0.6

and P(B)=0.55

Now,

Clearly,

Therefore taking Art class and taking French class are not independent events because P(A|B)≠P(A) and P(B|A)≠P(B) .[ By definition of independent events]

a complex number is a number that can be expressed in the form a + bi, where a and b are real numbers, and i is a solution of the equation x2 = −1. because no real number satisfies this equation, i is called an imaginary number. has no real solution, since the square of a real number cannot be negative.

the answer is b.)

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