# Math Help - card shuffle

1. ## card shuffle

Hello everyone!

You have 9 cards with the one of the numbers 1-9 written on each and they are shuffled, you pick a card and write down the number and this is the tens digit of a 2-digit number, then you put the card back. You pick another card and this number is the units digit. so you might have a number like 27 if you pik a 2 then a 7.

1. what's the probability of getting a number under 20?
2. whats teh probability of getting a 14?

thank you for reading my post

2. Originally Posted by Sweeties
Hello everyone!

You have 9 cards with the one of the numbers 1-9 written on each and they are shuffled, you pick a card and write down the number and this is the tens digit of a 2-digit number, then you put the card back. You pick another card and this number is the units digit. so you might have a number like 27 if you pik a 2 then a 7.

1. what's the probability of getting a number under 20?
2. whats teh probability of getting a 14?

thank you for reading my post
1. Well then your first card must be a 1. The probability of that happening is $\frac{1}{9}$

2. $\frac{1}{9}$ to get a 1. and $\frac{1}{9}$ to get a 4. Multiply them to get a probability of $\frac{1}{81}$

EDIT: Sorry, i missed the part about "replacing" the card. Thanks Plato.

3. Originally Posted by janvdl
2. $\frac{1}{8}$ to get a 4.
Think about that. Note the first card is put back into the deck.

4. Hello, Sweeties!

You have 9 cards with the one of the numbers 1-9 written on each.
They are shuffled, you pick a card and write down the number
. . This is the tens-digit of a two-digit number.
You replace the card and pick another card.
. . This is the units-digit of the two-digit number.

1. What's the probability of getting a number under 20?
2. What's the probability of getting a 14?

You can pick any of 9 numbers for the tens-digit.
You can pick any of 9 numbers for the units-digit.
. . There are: . $9 \times 9 \:=\:{\bf 81}$ possible two-digit numbers.

How many are under 20?
. . Well, there is: . $11,\,12,\,13,\,14,\,15,\,16,\,17,\,18,\,19$

Get the idea?

5. Originally Posted by Soroban
Hello, Sweeties!

You can pick any of 9 numbers for the tens-digit.
You can pick any of 9 numbers for the units-digit.
. . There are: . $9 \times 9 \:=\:{\bf 81}$ possible two-digit numbers.

How many are under 20?
. . Well, there is: . $11,\,12,\,13,\,14,\,15,\,16,\,17,\,18,\,19$

Get the idea?

yes i think so, 9/81 = 1/9

thank you all!