Here is the histogram representing the probability distribution of $X$, where $X$ is the number of heads minus the number of tails when three fair coins are tossed.

Summary

• Probability Distribution:

  $x$	$P(X = x)$
  -3	$\frac{1}{8}$
  -1	$\frac{3}{8}$
  1	$\frac{3}{8}$
  3	$\frac{1}{8}$

• Probability $P(-3 \leq X \leq -1) = \frac{1}{2}$

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Related Questions

1. What is the probability that $X$ equals zero if we add it as an option?
2. How would the distribution change if four coins were tossed?
3. Can we generalize this approach for any number of coin tosses?
4. How is the concept of expectation related to this distribution?
5. What other distributions are common with similar probability experiments?

Tip

When calculating probabilities for symmetrical events, counting outcomes systematically helps ensure accuracy.