ANSWERS
a. Dependent
b. Independent
c. Independent
d. Dependent
Step-by-step explanation
Independent events are two or more events where the outcome of one does not affect the outcome of the other, while dependent events are the ones where the outcome of one affects the outcome of the other.
As a general rule, all events where we select two or more items from a set without replacement are dependent events. This is because when we do not replace the previous items, the probability of selecting the next items changes.
a. This is an example of selection without replacement. Let's suppose that we select an ace of diamonds in the first draw. When we want to draw the next card, we know that it is impossible for it to be an ace of diamonds, so the outcome of this second card is limited to not being the first card - i.e. the outcomes of the next draws are affected by the previous ones. Hence, this is a dependent event.
b. When rolling two separate dice, the outcome of each does not affect the outcome of the other. Hence, this is an independent event.
c. In this case, we can choose any type of car and we can select any brand of tire, with each outcome not being affected by the other. Hence, this is an independent event.
d. This example is similar to the one given in (a), but with baseball cards instead. Here we know that there are five cards and, assuming that there are all different cards, there is a 1/5 chance of selecting each. However, after the first card is drawn, there are 4 cards left and then there is a 1/4 chance of selecting each. In other words, when the first card is selected without replacement, this affects the outcome of the second card. Hence, this is a dependent event.