Question

A fair coin is tossed three times in succession. The set of equally likely outcomes is StartSet HHH comma HHT comma HTH comma THH comma HTT comma THT comma TTH comma TTT EndSet. Find the probability of getting exactly zero heads.
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Part 1
The probability of getting zero heads is
  
enter your response here.
​(Type an integer or a simplified​ fraction.)

Answer 1

When tossing a fair coin three times, the total number of possible outcomes is \(2^3 = 8\) since each toss has 2 possible outcomes (heads or tails).

The outcomes are:
- HHH
- HHT
- HTH
- THH
- HTT
- THT
- TTH
- TTT

To find the probability of getting exactly zero heads, we need to identify the outcomes that match this criterion. The only outcome with zero heads is:
- TTT

So there is 1 favorable outcome (TTT) out of 8 possible outcomes.

To calculate the probability of getting exactly zero heads, we use the formula:

\[
P(\text{zero heads}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \frac{1}{8}
\]

Thus, the probability of getting zero heads is:

\[
\frac{1}{8}
\]