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James lives in San Francisco and works in Mountain View. In the morning, he has 3 transportation options (bus, cab, or train) to work, and in the evening he has the same 3 choices for his trip home.
If James randomly chooses his ride in the morning and in the evening, what is the probability that he'll take the same mode of transportation twice?

James lives in San Francisco and works in Mountain View. In the morning, he has $3$ transportation options (bus, cab, or train) to work, and in the evening he has the same $3$ choices for his trip home. $\newline$ If James randomly chooses his ride in the morning and in the evening, what is the probability that he'll take the same mode of transportation twice?

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Find probabilities using the addition rule

Full solution

Q. James lives in San Francisco and works in Mountain View. In the morning, he has

3

transportation options (bus, cab, or train) to work, and in the evening he has the same

3

choices for his trip home.

\newline

If James randomly chooses his ride in the morning and in the evening, what is the probability that he'll take the same mode of transportation twice?

Question Prompt: question_prompt: What's the chance James takes the same ride to and from work?
Total Combinations: He's got $3$ options for the morning and $3$ for the evening, so total combinations for both trips are $3 \times 3$ , which is $9$ .
Same Mode Options: For taking the same mode twice, he can choose bus-bus, cab-cab, or train-train. That's $3$ ways he can do that.
Probability Calculation: So the probability is the number of ways he can take the same mode over the total combinations, which is $\frac{3}{9}$ .
Simplification: Simplify $\frac{3}{9}$ to $\frac{1}{3}$ , cuz both are divisible by $3$ .

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