Thread: Dependent Events

Morgan believes she has a 60% chance that she will be late for class if she misses the 8:00 bus. There is a 80% chance that she will miss the 8:00 bus on any day.

A) What is the probability that she will miss her bus tomorrow, but still be on time?

B) If there is a 90% chance that Morgan will be late, even if she catches the 8:00 bus, what is the probability that she will be late on any given day.


I know the formula I need to use, I just don't know which percentages go in which part of the formula? Would for part A this be correct??

p(A) =
p(B) = 80%
p(AandB)= 60%

p(AandB) = p(A) x p(B)
p(A) = 0.60/0.80
p(A) = 0.48 = 48%

Originally Posted by momofmaxncoop

Morgan believes she has a 60% chance that she will be late for class if she misses the 8:00 bus. There is a 80% chance that she will miss the 8:00 bus on any day.
A) What is the probability that she will miss her bus tomorrow, but still be on time?
B) If there is a 90% chance that Morgan will be late, even if she catches the 8:00 bus, what is the probability that she will be late on any given day.

Let be the event of being late to class.
Let be the event of missing the bus.
The statement “a 60% chance that she will be late for class if she misses the 8:00 bus” seems to me to mean “given that the bus is missed, she will be late for class”.
That is the way that I read the “If…then…” form.

So part a) asks

Originally Posted by momofmaxncoop

Morgan believes she has a 60% chance that she will be late for class if she misses the 8:00 bus. There is a 80% chance that she will miss the 8:00 bus on any day.

A) What is the probability that she will miss her bus tomorrow, but still be on time?

B) If there is a 90% chance that Morgan will be late, even if she catches the 8:00 bus, what is the probability that she will be late on any given day.


I know the formula I need to use, I just don't know which percentages go in which part of the formula? Would for part A this be correct??

p(A) =
p(B) = 80%
p(AandB)= 60%

No, you were told that P(A)= 80% and P(A|B) (probability A happens given that B happens) is 60%. P(A and B) = P(A|B)*P(B). However, "A" here is "she will be late for class". You want P(A* and B) where A* is the complement of A, the probability that she is NOT late for class. If P(A|B)= 80% what is P(A*|B)?

p(AandB) = p(A) x p(B)
p(A) = 0.60/0.80
p(A) = 0.48 = 48%

Originally Posted by HallsofIvy

No, you were told that P(A)= 80% and P(A|B) (probability A happens given that B happens) is 60%. P(A and B) = P(A|B)*P(B). However, "A" here is "she will be late for class". You want P(A* and B) where A* is the complement of A, the probability that she is NOT late for class. If P(A|B)= 80% what is P(A*|B)?

Halls you seem to be agreeing with my reading of this. But why?
Mind you I think we are both right.
I just cannot find a definitive justification of it

@Plato... I too agree with your statement The statement “a 60% chance that she will be late for class if she misses the 8:00 bus” seems to me to mean “given that the bus is missed, she will be late for class”. But, won't the A part of the question ask for the p(A*|B) , that is the probability of the student being on time despite missing the bus, ?

Originally Posted by MAX09

The statement “a 60% chance that she will be late for class if she misses the 8:00 bus” seems to me to mean “given that the bus is missed, she will be late for class”. But, won't the A part of the question ask for the p(A*|B) , that is the probability of the student being on time despite missing the bus, ?

That is correct. Part a) wants the value of
But that is .

From part b) we are given .
Then asked to find .

Note that in general .
BUT

Originally Posted by Plato

I am posting this because I simply do not know how one reads the English here.
Let be the event of being late to class.
Let be the event of missing the bus.
The statement “a 60% chance that she will be late for class if she misses the 8:00 bus” seems to me to mean “given that the bus is missed, she will be late for class”.
That is the way that I read the “If…then…” form.

One the other hand, it seems reasonable to argue that the phrase means and, as in

Does anyone have a point view on this difference?
If so, can you support that point of view?

I was reading it exactly like you were, that is why I was asking for help and feedback on how about going on to answer the question.

Originally Posted by momofmaxncoop

I was reading it exactly like you were, that is why I was asking for help and feedback on how about going on to answer the question.

See reply #6.