Use the table to answer the question.
Probability of
Event #1 Probability of
Event #2 Probability of
Event #1 and Event #2
With Replacement A B 47⋅37
Without Replacement C D 47⋅36
Suppose you have seven cards—four are white and three are orange. You randomly draw two cards.
Event #1: drawing a white card
Event #2: drawing an orange card
Compare and contrast the probability of Event #1 and Event #2 if the events are independent and if the events are dependent. Which of the following is true?
(1 point)
Responses
The probabilities of cells A and C are the same, and the probabilities of the dependent events are higher.
The probabilities of cells A and C are the same, and the probabilities of the dependent events are higher.
The probabilities of cells B and D are the same, and the probabilities of the dependent events are higher.
The probabilities of cells B and D are the same, and the probabilities of the dependent events are higher.
The probabilities of cells B and D are the same, and the probabilities of the independent events are higher.
The probabilities of cells B and D are the same, and the probabilities of the independent events are higher.
The probabilities of cells A and C are the same, and the probabilities of the independent events are higher.
The probabilities of cells A and C are the same, and the probabilities of the independent events are higher.
When the events are independent (with replacement), the probability of drawing a white card and then an orange card would be calculated as P(Event #1) * P(Event #2) = (4/7) * (3/7) = 12/49. This is higher than 47/37.
When the events are dependent (without replacement), since you are not replacing the first card drawn, the chances of drawing an orange card after drawing a white card decreases, leading to a lower probability of the combined events.