Suppose you roll a standard number cube once. Are rolling a 4 and rolling a 3 mutually exclusive events? Explain.
Yes, rolling a 4 and rolling a 3 are mutually exclusive events because it is not possible to roll a single number that is both 4 and 3 at the same time. When you roll a standard number cube once, there are six possible outcomes, which are represented by the numbers 1, 2, 3, 4, 5, and 6. Since rolling a 4 and rolling a 3 are two different possible outcomes, they cannot occur simultaneously in a single roll of the dice. Therefore, these events are mutually exclusive.
To determine if rolling a 4 and rolling a 3 are mutually exclusive events, we need to understand what it means for two events to be mutually exclusive. Two events are considered mutually exclusive if they cannot happen at the same time, meaning if one event occurs, the other event cannot occur.
In this case, rolling a 4 and rolling a 3 are mutually exclusive events because a standard number cube only has six sides, numbered from 1 to 6. Since the number cube cannot show both a 4 and a 3 on the same roll, rolling a 4 and rolling a 3 cannot happen simultaneously. Therefore, these events are considered mutually exclusive.
To determine if rolling a 4 and rolling a 3 are mutually exclusive events, we need to understand what mutually exclusive means. Two events are considered mutually exclusive if they cannot both occur at the same time.
In this case, rolling a 4 and rolling a 3 on a standard number cube are mutually exclusive events. This is because the number cube only has one face with the number 4 and one face with the number 3. When you roll the number cube, only one of these numbers can be facing up at a time, making it impossible for both events to occur simultaneously.
In general, when two events have no outcomes in common, they are considered mutually exclusive. This means that if one event happens, the other event cannot happen. Rolling a specific number on a standard number cube is a clear example of mutually exclusive events because each number is represented on only one face of the cube.