AI tutor
Welcome to Bytelearn!
Let’s check out your problem:
Elizabeth lives in San Francisco and works in Mountain View. In the morning, she has transportation options (take a bus, a cab, or a train) to work, and in the evening she has the same choices for her trip home.If Elizabeth randomly chooses her ride in the morning and in the evening, what is the probability that she'll use a cab exactly one time?
Full solution
Q. Elizabeth lives in San Francisco and works in Mountain View. In the morning, she has transportation options (take a bus, a cab, or a train) to work, and in the evening she has the same choices for her trip home.If Elizabeth randomly chooses her ride in the morning and in the evening, what is the probability that she'll use a cab exactly one time?
- Options Combinations: Elizabeth has options in the morning and options in the evening, making a total of possible combinations for her round trip.
- Morning and Evening Cabs: To use a cab exactly once, Elizabeth can either take a cab in the morning and not in the evening, or not take a cab in the morning and take it in the evening.
- Probability Calculation: The probability of taking a cab in the morning and not in the evening is (for the cab in the morning) * (for not taking the cab in the evening).
- Total Probability Calculation: The probability of not taking a cab in the morning and taking it in the evening is also (for not taking the cab in the morning) * (for the cab in the evening).
- Total Probability Calculation: The probability of not taking a cab in the morning and taking it in the evening is also (for not taking the cab in the morning) * (for the cab in the evening).Adding these two probabilities together gives us the total probability of using a cab exactly once: .
- Total Probability Calculation: The probability of not taking a cab in the morning and taking it in the evening is also (for not taking the cab in the morning) * (for the cab in the evening).Adding these two probabilities together gives us the total probability of using a cab exactly once: .Calculating this, we get .
