Final answer:
For calculating probabilities involving 3 independent events with multiple potential outcomes, the number of total outcomes is determined by multiplying the outcomes for each individual event. If each event has two possible outcomes, the total possible outcomes are 8. If each event has three outcomes, as the question hints, the total possible outcomes are 27, as per option d).
Step-by-step explanation:
If we are calculating probabilities that involve 3 independent events, and each event can occur in multiple ways, we simply multiply the number of outcomes for each event to get the total number of possible outcomes. For instance, if you toss one fair coin, there are 2 possible outcomes: either Heads (H) or Tails (T). Then, if you also toss one fair, six-sided die, the die has 6 possible outcomes, which are 1, 2, 3, 4, 5, or 6. To find the total possible outcomes when combining these two separate events, you multiply their individual number of outcomes: 2 (coin) * 6 (die) = 12 possible outcomes.
However, if the question is referring to three separate events, each with two possible outcomes (such as flipping a coin), then the calculation would be 2 * 2 * 2, resulting in 8 possible outcomes. If an event has more than two outcomes, you would multiply the number of outcomes for each event accordingly.
From the options provided: a) 3, b) 6, c) 9, d) 27, the correct option is not listed because, based on simple probability rules, three events with at least two outcomes each would yield 2^3 = 8 or more outcomes depending on the number of outcomes of the third event. However, if all three events each have 3 possible outcomes, then the calculation follows 3 * 3 * 3, which equals 27 total outcomes. Therefore, the only valid option closest to our calculation is d) 27, provided each event has three distinct outcomes.