Probability Method? (chance of picking recipe sheet)

Hello it has been a while since I have done Maths.

I recently the read the following and was wondering if anyone knew why/how they get the figures they do?

If you have 100 recipe sheets. And, 10 of these sheets are linked because they all contain the same ingredient. The chance of picking a recipe sheet on it's own with that specific ingredient is 0.408 (Why?). But, the probability of all 10 sheets picked having the same ingredient is 5.77*10^-14. (Why?)

I don't understand why this should be the case.

If anyone can help I would be very grateful.
Thank You

Re: Probability Method?

Hello, sdslrn123!

Could you provide the original wording of the problem?
Some parts are missing information . . .
\(\displaystyle \;\;\)and I don't agree with their answers.

You have 100 recipe sheets.
And 10 of these sheets are linked because they all contain the same ingredient.

Click to expand...

Reality check
There are 100 sheets.
Ten of them are Linked; the other ninety are Not Linked . . . right?

The chance of picking a recipe sheet on its own with that specific ingredient is 0.408 \(\displaystyle \;\)(Why?)

Click to expand...

Not sure what "on its own" means . . .

So we are picking one sheet . . . right?

The probability of picking a Linked sheet is: \(\displaystyle \,P(Linked)\:=\:\frac{10}{100}\:=\:0.1\)

\(\displaystyle \;\;\)So what was the original question?

But the probability of all 10 sheets picked having the same ingredient is 5.77*10^-14 \(\displaystyle \;\)(Why?)

Click to expand...

Now it seems that we are picking ten sheets . . . right?

There are: \(\displaystyle \,C(100,10)\,=\,1.731030946\,\times\,10^{13}\) ways to pick 10 sheets.

There is one way to pick 10 sheets and get the 10 Linked sheets.

\(\displaystyle P(10\,Linked) \:=\:\frac{1}{1.731030946\,\times\,10^{13}} \;= \;5.776904235\,\times\,10^{-14} \;\approx\;5.7\)8\(\displaystyle \,\times\,10^{-14}\)

Re: Probability Method?

sdslrn123 said:

If you have 100 recipe sheets. And, 10 of these sheets are linked because they all contain the same ingredient. The chance of picking a recipe sheet on it's own with that specific ingredient is 0.408 (Why?). But, the probability of all 10 sheets picked having the same ingredient is 5.77*10^-14. (Why?)

Click to expand...

Surely the question means: Chose 10 and get 1 with a specific ingredient.
\(\displaystyle \L
\frac{{\left( \begin{array}{c}
90 \\
9 \\
\end{array} \right)\left( \begin{array}{c}
10 \\
1 \\
\end{array} \right)}}{{\left( \begin{array}{c}
100 \\
10 \\
\end{array} \right)}} = 0.40799\)

Generally, when you post the same question in multiple locations, it serves only to irritate those who visit both sites. It does NOT get you a faster response. Please be more considerate.

Welcome! by the way...