4 Which events are independent Select each correct answer Tw

4.

Which events are independent?

Select each correct answer.

Two six-sided number cubes are rolled.

Two blue cards are drawn from the bag without replacement.

Three coins are tossed at the same time.

Three red marbles are drawn from a bag with replacement.

Solution

Two or more events are independent, if the outcome of one event has no effect on the outcome of the other.

1. Two six numbered cubes are rolled is independent because the outcome of the first roll doesn\'t affect the outcome of the second.

2. Two blue cards are drawn from the same bag without replacement isn\'t independent because once the two cards are removed from the bag for the first event and not replaced, the number of blue cards in the bag is reduced thereby effecting the outcome of the second draw of blue cards.

3. Three coins are tossed at the same time is independent because the outcome of the second event is not effected by the first as the same coins are tossed every time keeping the probability constant.

4. Similarly, three red marbles drawn from a bag with replacement is independent.

So, the correct answers are 1,3,4.