elizabeth lives in san francisco and works in mountain view. in the morning, she has 3 transportation…

elizabeth lives in san francisco and works in mountain view. in the morning, she has 3 transportation options (take a bus, a cab, or a train) to work, and in the evening she has the same 3 choices for her trip home. if elizabeth randomly chooses her ride in the morning and in the evening, what is the probability that shell use a cab exactly one time?

elizabeth lives in san francisco and works in mountain view. in the morning, she has 3 transportation options (take a bus, a cab, or a train) to work, and in the evening she has the same 3 choices for her trip home. if elizabeth randomly chooses her ride in the morning and in the evening, what is the probability that shell use a cab exactly one time?

Answer

Explanation:

Step1: Calculate total number of combinations

The total number of ways to choose transportation in the morning and evening is $3\times3 = 9$ since there are 3 options in the morning and 3 options in the evening.

Step2: Calculate favorable cases

Case 1: Cab in the morning and non - cab in the evening. There is 1 way to choose a cab in the morning and 2 ways to choose non - cab (bus or train) in the evening. Case 2: Non - cab in the morning and cab in the evening. There are 2 ways to choose non - cab (bus or train) in the morning and 1 way to choose a cab in the evening. The total number of favorable cases is $1\times2+2\times1=4$.

Step3: Calculate probability

The probability $P$ of using a cab exactly one time is the number of favorable cases divided by the total number of cases. So $P=\frac{4}{9}$.

Answer:

$\frac{4}{9}$