You pick a number between 1,000 and 5,000. Then you flip a coin. Identify if these two events are independent or dependent. Explain.
The two events are independent. The number chosen and the result of the coin flip do not have any influence on each other. The result of the coin flip is completely random and does not affect the probability of selecting any particular number between 1,000 and 5,000. Likewise, the selection of a number does not influence the outcome of the coin flip. Therefore, the two events are independent of each other.
The events in this scenario are picking a number between 1,000 and 5,000 and flipping a coin. To determine if these events are independent or dependent, we need to understand the concept of independence in probability.
Two events are considered independent if the outcome of one event does not affect the outcome of the other. In other words, the probability of one event occurring remains the same regardless of whether the other event happens or not.
In this case, it is safe to assume that the number you pick between 1,000 and 5,000 and the outcome of flipping the coin are independent events. The reason is that there is no inherent connection or influence between choosing a number and flipping a coin.
Picking a number between 1,000 and 5,000 does not impact the outcome of flipping a coin, and vice versa. Consequently, the events are independent of each other.