# Math Help - Airplane departures and arrival stats

1. ## Airplane departures and arrival stats

Given that a flight departs (on-time) = P(d)=.83, and arrives (on-time) = P(a)=.82...and prob that it departs & arrives on time is .78:

1. what is the prob. that an aircraft will arrive on time or depart on time?
- ???
2. Are these events (a,d) independent?
- I said they are dependent upon eachother...but mabe I misintrepreted this....- the latter would only be correct if it was the same plane so what is correct?
3. If after a couple of years P(a)=.9 & p(d)=.85 and P(a and d)=.77 are we able to say that these events are mutually exclusive? or independent? Why or why not?
- I said they are mutually exclusive because they cannot occur at same time...but again is my interpretation wrong...we may not be talking about the same aircraft here. How should this be handled?

2. Draw a probability tree.

First branch up: depart on time, down, not depart on time.
Second branch following depart on time, up arrive on time and down not arrive on time.
Third branch following not depart on time, up arrive on time and down not arrive on time.

Complete the probability tree.

1. P(arrive or depart on time) = (P(arrive on time) x P(not depart on time) + (P(not arrive on time) x P(depart on time))

2. They are dependent. The fact that the plane (yes, the same plane) departure late/before due will affect the arrival time. And if you completed the probability tree correctly, you'll see that the probability that the plane does not arrive on time is different when the plane departs on time and when the plane does not.

3. The simple fact that $P(A \cap B)$ shows that they are NOT mutually exclusive.
From a new probability tree, we see that the two events are still dependant.

3. Yes, but with respect to the 1st question only, isn't the probability just 0.78 as we are told in the given intial conditions probability is... see original given initial cond. - or is it because the question asks or instead of "And". My answer is that the prob for question 1 is 0.78. Wrong?

4. Yes, if you draw the probability tree, you see everything.

As I told you, the probability that the plane arrives on time is dependent on whether the plane departed early or not.

The total probability is given, but that's not the individual probability when the plane departs late, or when the plane departs on time,