Question

Filip goes to a movie theater on weekends. On any given weekend, there is a 50% chance he will buy popcorn, there is a 40% chance he will buy juice, and there is a 20% chance he will buy both popcorn and juice. Mathematically determine whether the two events "buy popcorn" and "buy juice" are independent events. Enter 1 for dependent or 2 for independent.

Answer 1

To determine whether the events "buy popcorn" and "buy juice" are independent, we need to check if the following condition holds:

P(Popcorn and Juice) = P(Popcorn) * P(Juice)

From the problem, we have:

• P(Popcorn) = 0.5
• P(Juice) = 0.4
• P(Popcorn and Juice) = 0.2

Now, we calculate the product of the probabilities of buying popcorn and buying juice:

P(Popcorn) * P(Juice) = 0.5 * 0.4 = 0.2

Now we compare this value with P(Popcorn and Juice):

P(Popcorn and Juice) = 0.2

Since P(Popcorn and Juice) = P(Popcorn) * P(Juice), the two events are independent.

Thus, the answer is 2 for independent events.