Solution:
We are required to determine which of the events given in the options are NOT independent?
Note: Not independent in another words means dependent.
Thus, the question is asking us to pick the option that is dependent.
Firstly, let us look at what dependent events are.
Events are dependent if the outcome of one event affects the outcome of another. For example, if you draw two colored balls from a bag and the first ball is not replaced before you draw the second ball then the outcome of the second draw will be affected by the outcome of the first draw.
Now that we understand what dependent events are, let us use that knowledge to select the correct option
(1) A coin is tossed twice in a row.
The outcome of the second throw is not affected by the first throw. Thus, these events are independent
(2) A red jelly bean is taken from one jar and a yellow jelly bean is taken from another jar:
The outcome of the yellow jelly bean taken from one jar is not affected by A red jelly bean is taken from another jar. Thus, these events are independent
(3) A card is drawn from a standard deck, and then another card is drawn without the first one being replaced.
Since the first card drawn is not replaced, the other cards drawn will be dependent on the type of card drawn in the first draw. Thus, these events are dependent
(4) A bag contains 2 red marbles, 5 blue marbles, and 3 green marbles. A marble is picked and then placed back in the bag. Then another marble is picked.
Since the first marble picked is replaced before picking the second one, the second draw will not be affected by the first draw. Hence, these events are independent
Conclusion:
The correct answer is the third option. That is "A card is drawn from a standard deck, and then another card is drawn without the first one being replaced"