Answered

Discover new information and get your questions answered with IDNLearn.com. Discover reliable answers to your questions with our extensive database of expert knowledge.

Select the correct answer.

The probability that Edward purchases a video game from a store is 0.67 (event [tex]A[/tex]), and the probability that Greg purchases a video game from the store is 0.74 (event [tex]B[/tex]). The probability that Edward purchases a video game (given that Greg has purchased a video game) is 0.67.

Which statement is true?
A. Events [tex]A[/tex] and [tex]B[/tex] are independent because [tex]P(A \mid B) = P(A)[/tex]
B. Events [tex]A[/tex] and [tex]B[/tex] are dependent because [tex]P(A \mid B) = P(A)[/tex]
C. Events [tex]A[/tex] and [tex]B[/tex] are independent because [tex]P(A \mid B) = P(B)[/tex]
D. Events [tex]A[/tex] and [tex]B[/tex] are dependent because [tex]P(A \mid B) \neq P(A)[/tex]

Sagot :

GinnyAnsweridn
To determine whether events [tex]\( A \)[/tex] and [tex]\( B \)[/tex] are independent or dependent, we need to compare the probability [tex]\( P(A \mid B) \)[/tex] (the probability that Edward purchases a video game given that Greg has purchased a video game) with [tex]\( P(A) \)[/tex] (the probability that Edward purchases a video game).

Given:
- [tex]\( P(A) = 0.67 \)[/tex] (the probability that Edward purchases a video game)
- [tex]\( P(B) = 0.74 \)[/tex] (the probability that Greg purchases a video game)
- [tex]\( P(A \mid B) = 0.67 \)[/tex] (the probability that Edward purchases a video game, given that Greg has purchased a video game)

Events [tex]\( A \)[/tex] and [tex]\( B \)[/tex] are independent if and only if:
[tex]\[ P(A \mid B) = P(A) \][/tex]

In this case:
[tex]\[ P(A \mid B) = 0.67 \][/tex]
[tex]\[ P(A) = 0.67 \][/tex]

Since [tex]\( P(A \mid B) \)[/tex] equals [tex]\( P(A) \)[/tex], the events [tex]\( A \)[/tex] and [tex]\( B \)[/tex] are independent.

Therefore, the correct statement is:

A. Events [tex]\( A \)[/tex] and [tex]\( B \)[/tex] are independent because [tex]\( P(A \mid B) = P(A) \)[/tex]
Thank you for participating in our discussion. We value every contribution. Keep sharing knowledge and helping others find the answers they need. Let's create a dynamic and informative learning environment together. Your questions deserve accurate answers. Thank you for visiting IDNLearn.com, and see you again for more solutions.