Question

A group 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) .<<<<<<<

Answer 1

Answer:

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:

Answer 2

Answer: 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 :-

$P(A|B)=\dfrac{P(A\cap B)}{P(B)}$

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

$P(\cap B)=0.2$

Now, $P(A|B)=\dfrac{0.2}{0.55}=0.036363\approx0.036$

$P(B|A)=\dfrac{P(A\cap B)}{P(A)}=\dfrac{0.2}{0.6}=0.33333\aprox0.333$

Clearly, $P(A|B)\neq P(A)$

$P(B|A)\neq P(B)$

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]