Conditional and Mutually Exclusive?

Hello,

I am struggling with this question:

You will have to take a test on one of the following days next week. Here are the probabilities: (will take/won't take)

Monday 50/50
Tuesday 75/25
Wednesday 90/10
Thursday 95/5

What is the probability that you will have taken the test by Friday?

I really am stuck on this one, so any wisdom is appreciated.

Thanks,
Laura

lejanco said:

Hello,

I am struggling with this question:

You will have to take a test on one of the following days next week. Here are the probabilities: (will take/won't take)

Monday 50/50
Tuesday 75/25
Wednesday 90/10
Thursday 95/5

What is the probability that you will have taken the test by Friday?

I really am stuck on this one, so any wisdom is appreciated.

Thanks,
Laura

Click to expand...

You can look at this several ways but I think the right way is to interpret the statements as
-Monday the probability is 50% the test will be given.
-Tuesday the probability that the test will either have been given before today or today is 75%.
-Wednesday the probability that the test will either have been given before today or today is 90%.
-Thursday the probability that the test will either have been given before today or today is 95%.

So I would say that, since the test will be given on one of the following days next week, the probability that the test will have been given by (and excluding) Friday is 95% and the probability that the test will have been given by (and including Friday) is 100%.

EDIT: That is, you are looking at a cumulative probability, not a conditional nor mutually exclusive proability.

Thanks. I ended up using a probability tree and got 99.997.

I interpret the information you give a little differently from Ishuda. I presume that, by these numbers, you mean there is a "50-50" chance the test will be given on Monday and if it isn't there will be a "75-25" chance it will be given on Tuesday, etc. Here's how I would do this problem:

Imagine 1000000 such situations. In half of those, 500000, the test will be given on Monday. Of the remaining 500000, in 75% of them, 375000, the test will be given on Tuesday. That leaves 125000 situations in which the test is not given on Monday or Tuesday. In 90% or those, 112500, the test is given on Wednesday. That leaves 12500 situations. In 95% of those, 11875, the test is given on Thursday. So, out of the 1000000 situations, the test is given before Friday, so that you will have "taken the test by Friday" on 500000+ 375000+ 112500+ 11875= 999375. That is \(\displaystyle \frac{999375}{1000000}= 0.999375\) or 99.9375%

HallsofIvy said:

I interpret the information you give a little differently from Ishuda. ...

Click to expand...

Yeah, and I was going to do something like that until I realized what I would have to do to work it out so I chose the easier way. Besides, I don't always do that well at sadistics.