The astrology software package, Turbo Kismet,† works by first generating random number sequences and then interpreting them numerologically. When I ran it yesterday, it informed me that there was a 1/3 probability that I would meet a tall dark stranger this month, a 2/3 probability that I would travel this month, and a 1/12 probability that I would meet a tall dark stranger and also travel this month. What is the probability that I will either meet a tall dark stranger or travel this month? HINT [See Quick Example 14.] (Enter your probability as a fraction.)

The problem is asking for the probability that you will either meet a tall dark stranger or travel this month. To solve this, we can use the principle of inclusion-exclusion for probabilities.

Let:

- \( P(A) \) be the probability that you meet a tall dark stranger this month. According to the problem, \( P(A) = \frac{1}{3} \).
- \( P(B) \) be the probability that you travel this month. According to the problem, \( P(B) = \frac{2}{3} \).
- \( P(A \cap B) \) be the probability that you both meet a tall dark stranger and travel this month. According to the problem, \( P(A \cap B) = \frac{1}{12} \).

The probability that either event happens (meeting a tall dark stranger or traveling) is given by the formula:

\[
P(A \cup B) = P(A) + P(B) - P(A \cap B)
\]

Substituting the values:

\[
P(A \cup B) = \frac{1}{3} + \frac{2}{3} - \frac{1}{12}
\]

First, add the probabilities for meeting a tall dark stranger and traveling:

\[
\frac{1}{3} + \frac{2}{3} = 1
\]

Now, subtract the probability of both events happening:

\[
P(A \cup B) = 1 - \frac{1}{12}
\]

Convert 1 to a fraction with a denominator of 12:

\[
1 = \frac{12}{12}
\]

Now subtract:

\[
P(A \cup B) = \frac{12}{12} - \frac{1}{12} = \frac{11}{12}
\]

Thus, the probability that you will either meet a tall dark stranger or travel this month is:

\[
\boxed{\frac{11}{12}}
\]

Do you need any further details or explanations?

Here are 5 related questions:
1. What is the inclusion-exclusion principle in probability?
2. How do you calculate the probability of the complement of an event?
3. What is the probability of two independent events occurring together?
4. How does conditional probability differ from joint probability?
5. What is the significance of mutually exclusive events in probability?

**Tip:** When working with probabilities, always ensure that all fractions are simplified and that the total probability doesn't exceed 1.

Find out how to calculate the probability of either meeting a tall dark stranger or traveling this month using the inclusion-exclusion principle. This problem covers essential probability concepts and formulas, suitable for students in Grades 9-12.

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