Question When a coin is tossed three times, what is the probability that all three tosses are heads? The possible outcomes for the coin tosses are $$ \{H H H, T T T, H T T, H H T, T H H, T T H, H T H, T H T\} $$ - Express your answer as a simplified fraction.

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When a coin is tossed three times, each toss has two possible outcomes: heads (H) or tails (T). Therefore, the total number of possible outcomes when tossing the coin three times is calculated as follows:

$$
2^3 = 8
$$

The possible outcomes for the three tosses are:

1. H H H
2. H H T
3. H T H
4. H T T
5. T H H
6. T H T
7. T T H
8. T T T

Among these outcomes, we are interested in the event where all three tosses result in heads, which corresponds to the outcome H H H.

There is only 1 favorable outcome (H H H) out of the 8 possible outcomes. Therefore, the probability $$ P $$ of getting all heads when tossing the coin three times is given by the ratio of the number of favorable outcomes to the total number of outcomes:

$$
P(\text{all heads}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \frac{1}{8}
$$

Thus, the probability that all three tosses are heads is

$$
\boxed{\frac{1}{8}}
$$
The probability of all three tosses being heads is $$ \frac{1}{8} $$.

Question When a coin is tossed three times, what is the probability that all three tosses are heads? The possible outcomes for the coin tosses are \( \{H H H, T T T, H T T, H H T, T H H, T T H, H T H, T H T\} \) - Express your answer as a simplified fraction.

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