Question

alberta diploma question
alan places five white marbles and five black marbles into a bag. he then performs the two experiments described below to select two marbles from the bag.
first experiment
one marble is selected from the bag and replaced before a second marble is selected.
second experiment
one marble is selected from the bag and not replaced before a second marble is selected.
the following two events are the same for each experiment:
event x: the first marble selected is black.
event y: the second marble selected is white.
in the first experiment, event x and event y are select an answer, and in the second experiment, event x and event y are select an answer
question help: message instructor

Explanation:

Step1: Define independent and dependent events

Independent events: The occurrence of one event does not affect the probability of the other event. Dependent events: The occurrence of one event affects the probability of the other event.

Step2: Analyze the first - experiment

In the first experiment, a marble is selected and replaced before the second selection. The probability of Event Y (second marble is white) is not affected by whether Event X (first marble is black) occurs or not. Because after replacement, the composition of marbles in the bag remains the same. So, Event X and Event Y are independent.

Step3: Analyze the second - experiment

In the second experiment, a marble is selected and not replaced before the second selection. If Event X (first marble is black) occurs, then there are 9 marbles left in the bag for the second draw, with 5 white marbles. If Event X does not occur (first marble is white), then there are also 9 marbles left in the bag for the second draw, but with 4 white marbles. So, the probability of Event Y depends on whether Event X occurs or not. Thus, Event X and Event Y are dependent.

Answer:

In the first experiment, Event X and Event Y are independent. In the second experiment, Event X and Event Y are dependent.