Question

The probability that Evan purchases a comic book from the bookstore (event A) is 0.67, and the probability that Glen purchases a comic book from the bookstore (event B) is 0.74. The probability that both Evan and Glen purchase a comic book is 0.2442. Given this information, which statement is true?

A. Events A and B are independent because P(A|B) ≠ P(A).
  B.Events A and B are independent because P(A and B) = P(A) × P(B).
  C.Events A and B are dependent because P(A and B) ≠ P(A) × P(B).
  D.Events A and B are dependent because P(A|B) = P(A).

Answer 1

no the correct answer is c

Answer 2

Answer: Option 'C' is correct.

Explanation:

Since we have given that

Probability that Evan purchases a comic book from the bookstore (event A) = 0.67

Probability that Glen purchases a comic book from the bookstore (event B) = 0.74.

And,

Probability that both Evan and Glen purchase a comic book = 0.2442.

As we know that if two events i.e. A and B are independent then,

`P(A\cap B)=P(A).P(B)`

But here,

`0.67* 0.74\\eq 0.2442\\\\0.4958 \\eq 0.2442\\\\P(A).P(B)\\eq P(A\cap B)`

Therefore, the two events are dependent.

Hence, Option 'C' is correct.