[bradloff]

Hi all, I am trying to help my daughter with some probability homework. Unfortunately, I'm a bit rusty on these probability formulas, and I have limited notes/books to look at, as the teacher is not taking this from my daughters math book, and my daughters notes aren't too good! :confused:

Anyway, we are trying to calculate the probability of an event after an a previous event has already happened.

One example could be something like this:
There are 10 marbles, 2 white, 5 black, and 3 gray

Question, what is the probability of drawing a white marble from a bag if all marbles are put in the bag at the start? Ok, this one is easy, it is 2/10 or 1/5.

Now it gets interesting,

The marbles are not returned to the bag after drawing. What is the probability that the second marble is gray?

So, the issue I have is if the first marble drawn is gray, then the probability that the second marble is gray will be different than if a different color was drawn first.

Can anyone help me figure out the probability of the second marble being gray?

Thanks,
Brian

[Perito]

Anyway, we are trying to calculate the probability of an event after an a previous event has already happened.

There are 10 marbles, 2 white, 5 black, and 3 gray

What is the probability of drawing a white marble from a bag if all marbles are put in the bag at the start? Ok, this one is easy, it is 2/10 or 1/5.

The marbles are not returned to the bag after drawing. What is the probability that the second marble is gray?

So, the issue I have is if the first marble drawn is gray, then the probability that the second marble is gray will be different than if a different color was drawn first.

Can anyone help me figure out the probability of the second marble being gray?

The general subject is "Probability of dependent events".

The probability of drawing a gray marble in a second draw is dependent on what was drawn the first time. If a gray marble were drawn, the probability of drawing a second gray marble would be 2/9. If a gray marble has already been drawn, the probability of drawing a gray marble would be 3/9 or 1/3. Note that these are not overall probabilities. They're the probability of drawing a particular color in a second event. One of the big problems in probability is that people confuse what they're predicting.

Let me google that for you - Probability of dependent events

Usually, the question will be posed, "what's the probability of drawing two gray marbles" or "what's the probability of not drawing no white marbles". In the first case, it's 3/10 x 2/10. In the second case, you have to figure out the probability of not drawing a white marble (7/10 x 6/10).