Final answer:
To calculate the probabilities of compound events, use a systematic approach utilizing provided probability tables, determining the independence or dependence of events, and applying the addition or product rules. Supplementary angles can be expressed as x and 180-x, as their sum is always 180 degrees.
Step-by-step explanation:
To find the probabilities of any compound event, one must follow a systematic approach. This involves using probability tables thoroughly explained in Appendix H, which does not require the use of technology. The following steps outline the general procedure:
- Determine if the events are independent or dependent.
- For mutually exclusive events, use the addition rule: Add their individual probabilities.
- For events that can happen together (non-mutually exclusive), correct the addition by subtracting the probability of them happening simultaneously.
- If the events are independent, use the product rule: Multiply the probabilities of the individual events.
- When dealing with a conditional probability, adjust the probability of one event occurring in the context of the occurrence of the second event.
- Make use of tools such as contingency tables, Venn diagrams, and tree diagrams to organize and interpret the probabilities.
For supplementary angles, the two angles can be represented in terms of their measures as x and 180–x. Since the sum of supplementary angles is always 180 degrees, if one angle measures x degrees, the other must measure 180–x degrees to fulfill this condition.