Consider 6 different-color marbles that are randomly selected. Create a scenario for event A and a scenario for event B, such that P (A and B) = 30 . State the result of event A, the result of event B, and explain if the two events are independent or dependent. Use an example with something to do with ice cream, and write your answer out in paragraph form with high school grammar. Shorten answer to one paragraph.

Answer 1

Consider a scenario in an ice cream shop where a customer randomly selects 6 different-color marbles from a jar to use as toppings for their sundae. Let event A be the selection of at least one red marble, and let event B be the selection of at least one blue marble. If the probability of selecting at least one red marble is 0.5 and the probability of selecting at least one blue marble is also 0.5, then the probability of both events occurring together, P(A and B), is 0.3, indicating that the customer likely picks at least one marble of each color. Because the occurrence of selecting red marbles affects the chances of also selecting blue marbles (due to limited quantities or color combinations), events A and B are dependent events. This means the selection of one type of marble impacts the selection of the other, making the two events related rather than independent.