Question

A bag contains 3 marbles: one black, one red and one orange. 2 marbles are selected from the bag. Let Event A={first selection}, and Event B={second selection}. Which of the following ensures Event A and Event B are independent events?

1. after selecting the first marble, it is not placed back into the bag.
2. after selecting the second marble, it is not placed back into the bag.
3. after selecting the second marble, it is placed back into the bag.
4. after selecting the first marble, it is placed back into the bag.

Answer 1

The following ensures Event A and Event B are independent events:

d. after selecting the first marble, it is placed back into the bag.

Two events are said to be independent if if the incidence of one event does not affect the probability of the other event. Here since we place the first marble back in the bag after selecting it, the event of drawing the second marble will be independent of the outcome of the first draw.

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