Let's break down the problem step by step to fill out the table and calculate the probabilities for each event.

Event A: "Exactly one head"

We are looking for outcomes with only one occurrence of "H" (head). The outcomes listed are:

• HTT (one head) The probability is the number of favorable outcomes (1) divided by the total number of outcomes (8), so $P(A) = \frac{1}{8}$.

Event B: "Two or more tails"

We need outcomes that have at least two tails ("T"). The valid outcomes are:

• HTT
• TTT
• TTH These outcomes contain two or more tails. There are 3 such outcomes, so the probability $P(B) = \frac{3}{8}$.

Event C: "A tail on the first toss"

This event requires that the first toss results in a "T". The valid outcomes are:

• HTT
• TTT
• TTH
• THT These outcomes start with a tail. There are 4 such outcomes, so $P(C) = \frac{4}{8} = \frac{1}{2}$.

Filling out the table:

Let me know if you need further clarification or additional details.

5 Related Questions:

1. How do you calculate the probability of an event?
2. What is the sample space of a three-coin toss?
3. How do independent events affect probability calculations?
4. What is the difference between "mutually exclusive" and "independent" events in probability?
5. Can we calculate the probability of getting at least one tail in three coin tosses?

Tip:

When calculating probabilities for multiple events, always ensure the events are independent or mutually exclusive to avoid confusion.