Approximate probability

[Pecerudari]

One box contains 10 cards, three of which have the number 2 on them, five with the number 1 and two with the number 3. 100 cards are pulled out with returning. Find the approximate probability that the sum of the numbers on the cards will be betwern 160 and 200. PLS HELP

 

[pka]

One box contains 10 cards, three of which have the number 2 on them, five with the number 1 and two with the number 3. 100 cards are pulled out with returning. Find the approximate probability that the sum of the numbers on the cards will be betwern 160 and 200.

The probability is zero. It is impossible to pull 100 cards from a box containing only ten cards.

 

[Dr.Peterson]

The probability is zero. It is impossible to pull 100 cards from a box containing only ten cards.

Presumably "with returning" means what we more commonly call "with replacement" - that is, each card is put back in the box before taking the next. With this understanding, it is possible.

Now the question for Pecerudari is, what have you learned that might be of use here? And what specific help do you need? Be sure to read and follow the site's submission guidelines.

 

[pka]

Presumably "with returning" means what we more commonly call "with replacement" - that is, each card is put back in the box before taking the next. With this understanding, it is possible.

Oh brother, I read "100 cards are pulled out with returning" as 100 cards are pulled without returning ".
That said, I not sure what this question means. Consider pulling fifty ones, twenty twos, and thirty threes for a sum of 180.
That can happen in \(\displaystyle \frac{100!}{50!\cdot 20!\cdot 30!}\) Here is the calculation. That is a huge number with a minuscule probability.