You randomly draw 1 card from a standard deck of 52, and 1 card from another standard deck. What's the probability that the sum of the 2 cards is 7?

If you randomly take a positive integer and divide it by 23, what’s the probability that the remainder is 13?

You randomly draw 1 card from a standard deck of 52, and 1 card from another standard deck. What's the probability that the sum of the 2 cards is 7?

First think through all the possible combinations that add to 7. To succeed you might draw:

Ace + 6
2+ 5
3_+ 4
4 + 3
5 + 2
6 + Ace

The probability of drawing seven with two cards is equal to the sum of each of the probabilities pof each of these occurring. So let's start with the first possibility: ace + 6. The probabaility of drawing an ace from the first deck is 4/52, and the probability of drawing two from the second deck is also 4/52. Do you see what that is? Hence the probability of drawing BOTH an ace and two is:

P(Ace + 2) = \frac 4 {52} \times \frac 4 {52} \ = \ \frac {16} {2704} = \frac 1 {169}


Now repeat this for the other 5 cases, and add them up. What do you get?

If you randomly take a positive integer and divide it by 23, what's the probability that the remainder is 13?

Please do not post two separate questions in the same thread - it's best to start a new thread for each question.

If you divide a number by 23, the possible values for the remainder is:

0, 1, 2, 3,. 20, 21, or 22

Note there are 23 possible outcomes. So now can you take it from here? What's the probability of one of those outcomes (13) happening?