Hi! So this question kind of has two parts to it. If someone could help me with this, that would be great! Thanks! :)
Juan lives in a large city and commutes to work daily by subway or taxi. He takes the subway 80% of the time because it costs less and he takes a taxi 20% of the time because it saves time. When taking the subway, he arrives at work on time 70% of the time.
Question A: What is the probability that Juan took the subway and is at work on time any given day?
Question B: The probability that Juan took a taxi and arrived on time is 18%.
Knowing that he takes a taxi 20% of the time, what is the probability that the taxi arrived on time.
BECUSE IS NOMALY EASY FOR ME WHEN I ADD
If the events are independent, the probability of both/all events occurring is determined by multiplying the probabilities of the individual events.
A. .8 * .7 = ?
B. .2 * ? = .18
Juan lives in a large city and commutes to work daily by subway or by taxi. He takes the subway 80% of the time because it costs less, and he takes a taxi the other 20% of the time. When taking the subway, he arrives at work on time 70% of the time, whereas he makes it on time 90% of the time when traveling by taxi.
To answer both parts of the question, we can use conditional probability.
Question A: What is the probability that Juan took the subway and is at work on time any given day?
To find the probability that Juan took the subway and is at work on time, we need to multiply the probabilities of two independent events: taking the subway (80% probability) and arriving on time when taking the subway (70% probability).
Probability (Subway and On Time) = Probability (Subway) * Probability (On Time | Subway)
= 0.8 * 0.7
= 0.56
Therefore, the probability that Juan took the subway and is at work on time any given day is 0.56, or 56%.
Question B: The probability that Juan took a taxi and arrived on time is 18%.
To find the probability that the taxi arrived on time, given that Juan took a taxi, we need to use conditional probability.
Probability (On Time | Taxi) = (Probability (Taxi and On Time)) / Probability (Taxi)
We know that Probability (Taxi) = 0.2 (since Juan takes a taxi 20% of the time), and the Probability (On Time | Taxi) = 0.18 (as given in the question).
Plugging in these values, we can calculate the Probability (Taxi and On Time):
Probability (Taxi and On Time) = Probability (On Time | Taxi) * Probability (Taxi)
= 0.18 * 0.2
= 0.036
Therefore, the probability that the taxi arrived on time, given that Juan took a taxi, is 0.036, or 3.6%.