A friend who works in a big city owns two cars, one small and one large. One-quarter of the time he drives the small car to work, and three-quarters of the time he takes the large car. If he takes the small car, he usually has little trouble parking and so is at work on time with probability 0.7. If he takes the large car, he is on time to work with probability 0.5. Given that he was at work on time on a particular morning, what is the probability that he drove the small car? (Give the answer to three decimal places.)

The probability that he drove the small car is 0.318.

Step-by-step explanation:

We are given that a friend who works in a big city owns two cars, one small and one large. One-quarter of the time he drives the small car to work, and three-quarters of the time he takes the large car.

If he takes the small car, he usually has little trouble parking and so is at work on time with probability 0.7. If he takes the large car, he is on time to work with probability 0.5.

Let the Probability that he drives the small car = P(S) = = 0.25

Probability that he drives the large car = P(L) = = 0.75

Also, let WT = event that he is at work on time

So, Probability that he is at work on time given that he takes the small car = P(WT / S) = 0.7

Probability that he is at work on time given that he takes the large car = P(WT / L) = 0.5

Now, given that he was at work on time on a particular morning, the probability that he drove the small car is given by = P(S / WT)

We will use the concept of Bayes' Theorem for calculating above probability;

So,    P(S / WT)  =  

                          =  

                          =  

                          =  0.318

Hence, the required probability is 0.318.

2? if not the correct answer you might need to provide more information

step-by-step explanation:

the central idea is that:

individuals should refuse to cooperate with institutions they believe unjust.

thoreau felt  that governments were more often agents of corruption than justice, even democracies, and that just because the majority feels a certain way does not make it just or correct in absolute terms. he uses the fact that slavery exists in our democracy to support this idea.

he goes on to say that, as a result, people should live true to their own internal laws regarding right and wrong, as a product of reflection and a moral life, rather than following every law that society imposes. 

step-by-step explanation: