Mathematics ACT Aspire Practice Test

How is probability defined in the context of simple events?

1. The ratio of successful outcomes to total outcomes

2. The total number of outcomes in a sample space

3. A measure of all possible results

4. Only the possible unfavorable outcomes

The correct answer is: The ratio of successful outcomes to total outcomes

In the context of simple events, probability is defined as the ratio of successful outcomes to total outcomes. This concept reflects the idea that probability quantifies the likelihood of a particular event occurring among all possible outcomes in a sample space. To elaborate, when determining the probability of a simple event, you identify the number of favorable outcomes, which are the specific outcomes that would result in the event of interest happening. Then, this number is divided by the total number of possible outcomes in the sample space, which includes every outcome that could possibly occur in the situation being analyzed. For example, if a single die is rolled, there are 6 possible outcomes (1 through 6), and if you want to find the probability of rolling a 3, there is only 1 successful outcome (rolling a 3). Therefore, the probability of this event would be 1 (successful outcome) divided by 6 (total outcomes), resulting in a probability of 1/6. The other choices do not accurately represent the concept of probability. The total number of outcomes in a sample space provides context but does not define probability itself. A measure of all possible results is too vague and does not specifically connect to how probability is calculated. Only considering unfavorable outcomes