Question

A group of people were asked if they enjoy going to concerts or movies.

The table shows the probabilities of the results.

Answer 1

The correct answer is the second choice.

They are not independent because P(movies|concerts)=0.25 ≠ P(movies)=0.6, and P(concerts|movies)=0.25 ≠ P(concerts)=0.55

Answer 2

Answer:

Option: B is the correct answer.

Enjoying movies and concerts are not independent since,

$P(movies|concerts)\neq P(movies)$

and  $P(concerts|movies)\neq P(concerts)$

Step-by-step explanation:

We know that if two events A and B are independent then:

$P(A\bigcap B)=P(A)\times P(B)$

where P denote the probability of an event.

Now, we know that:

$P(movies|concerts)=\dfrac{P(movies\bigcap Concerts)}{P(concerts)}$

Similarly:

$P(concerts|movies)=\dfrac{P(movies\bigcap Concerts)}{P(movies)}$

If movies and concerts are independent then:

$P(movies|concerts)=P(movies)$

Similarly:

$P(concerts|movies)=P(concerts)$

We have:

$P(movies)=0.6$

$P(concerts)=0.55$

$P(concerts|movies)=\dfrac{0.25}{0.6}$

$P(movies|concerts)=\dfrac{0.25}{0.55}$

Hence,

Enjoying movies and concerts are not independent

Since,

$P(movies|concerts)\neq P(movies)$

and  $P(concerts|movies)\neq P(concerts)$