james lives in san francisco and works in mountain view. in the morning, he has 3 transportation options…

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 hell 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. if james randomly chooses his ride in the morning and in the evening, what is the probability that hell take the same mode of transportation twice?

Answer

Explanation:

Step1: Calculate total combinations

The total number of ways to choose a transportation - mode in the morning and in the evening is the product of the number of morning choices and the number of evening choices. Since there are 3 choices in the morning and 3 choices in the evening, the total number of combinations is $3\times3 = 9$.

Step2: Calculate favorable combinations

The favorable cases (taking the same mode of transportation twice) are 3: (bus - bus, cab - cab, train - train).

Step3: Calculate probability

The probability $P$ of an event is the number of favorable outcomes divided by the number of total outcomes. So $P=\frac{3}{9}=\frac{1}{3}$.

Answer:

$\frac{1}{3}$