Morning Commute

The questions below are due on Tuesday April 16, 2019; 11:00:00 PM.

You are not logged in.
If you are a current student, please Log In for full access to this page.

After running late many days in a row, you decide to do some probabilistic modeling of your morning commute, in an effort to make sure you can always get to 6.01 on time :)

Let L be a random variable that takes value 1 if you are running late leaving the house, and 0 otherwise.
Let T be a random variable that takes value 1 if you get stuck behind a train, and 0 otherwise. (Assume we're at the far end of the E line where this will actually happen).
Let G be a random variable that takes value 1 if you get a green light at Vassar and Mass Ave, and 0 otherwise.

Consider the following table of probabilities:

	T=1	T=0
L=1	0.70	0.10
L=0	0.06	0.14

Enter a single number in each of the following boxes, accurate to three digits after the decimal point:

What is the probability that you are running late?

What is the probability that you get stuck behind a train, given that you are running late?

What is the total probability that you get stuck behind a train?

Assume that L and T are related as given in the table above, and that \Pr(G = 1 | T = 1) = 0.1 and \Pr(G = 1 | T = 0) = 0.2, regardless of the value of L.

What is the probability that you were stuck behind a train given that you got a green light at Vassar and Mass Ave?