I think you can do this using Bayes theorem but, as I can never be bothered to learn it, I prefer to make a probability tree diagram.

Working from left to right, we have the initial set up of 10 blacks and x white. Then either a black or white is added shown by the two branches.

Then we choose a ball which may be black or white. So a further two branches are shown for each of the branches already added.

The final outcomes are shown as 'its black' given 'black' and so on.

As we know the final ball is black we only have two branches to consider: P(b|b) and P(b|w). So I think the answer is

Hope that helps,

Bob

]]>I think I've seen this somewhere else, with a slightly different wording. I believe it says that the insect moves by jumps on a straight line and to the same direction.]]>

An hour ago on Yahoo Answers, the answer was posted.

It has to do with cell phone text messaging.

Have fun...

I am curious about this, but I have no clue. In text message, 896 results in twm, right? So, what is the pattern?

]]>You aren't spelling it right, it's spelled g-h-o-t-i.

Wow... I first heard about it in 9Gag, didn't know that it went back as far as 1855.

]]>Well, averages don't exist in real life... especially non-natural numbers. But all the same, averages are very interesting

What did you mean that averages don't exist in real life?

]]>What an odd problem, you don't often see

s in 'solve for x's

Trap questions. Sometimes they want to see if the students understand that anything^0 = 1.

]]>Ah, yes. Permutation and Combination. An interesting subject. Don't mean to be annoying... Theres a P & C calculator here, right?

Sometimes the matter is he doesn't know whether to use P or C. It's not that simple. Calculators can't help us if we don't even know which ones to use.

]]>Fussy teachers will prefer

I would replace "fussy" with "wrong", but perhaps it's just me.

Maybe the teacher is just someone with OCD who can't bear to see negative numbers.

]]>After getting more details i found that the total no. Of possibilities are 10C2 or C(10,2) =10!/(2!*8!)=45

bobbym and I both got 945 possibilities. The full list is a bit large to post, but in the hidebox below is a random sample of 50 from the list. The entries are in strict numerical order.

In post #14, my image in the 'level 5' hidebox shows the first 60 and the last 60 possibilities from the 945 (entries are in numerical order). 4 from the list of 50 random samples are in there too, so that makes 166 possibilities that I've posted.

They all seem to be valid to me, and if you check them I think you'll agree that there are many more possibilities than your answer of 45.

So I suppose there's an error in your formula, but I'm sorry, I don't know enough about this kind of maths to be able to show where it is.

]]>I can only give hints. My hands are bound.]]>

Welcome to the forum.

There's a formula for expected value which goes like this:

where the x's are the values and the p's are the probabilities. So you could take the x values using those midpoints and the probabilities by dividing the percentages by 100 and adding them together like this:

Some might argue that the midpoint is not 24.5 etc as you ought to be considering a continuum from 0 to 50 inclusive which would make the midpoint 25. In practice it doesn't make much difference as this is only a theoretical statistic.

You'll also have to make a judgement about what to use for A9.

Bob

]]>Welcome to the forum.

There's a difference here between the engineering problem where you actually want to get to the centre without getting your feet wet and the geometry problem where we assume that lines have zero 'thickness'. The dotted lines on my diagram show that you'd have to overlap the second plank on the first in order to make a secure platform. But I'll assume we meant to ignore that and take CD as 10 and the chord AB as 16.

It's a property of all circles that a line from the centre of the circle to the centre of any chord will be at right angles to the chord. In other words angle ADC is 90. So you can use Pythagoras theorem to calculate AC squared. Don't bother to find the square root because you want radius squared for the area. (pi r squared)

Hopefully that should be enough for you to complete the question.

Bob

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