Pick a card, any card!

Todays math lesson on probability was a little more challenging than last time. We used a deck of playing cards to practice probability. Some questions were easier like finding the probability of drawing a red card. Half of the deck is red so the probability of choosing a red  card was 26 over 52 which reduced to one half. 
Other questions were harder. One I had a hard time with asked to find the probability of drawing a red card or a 10. I solved it by finding the probability of each and adding them together. 
So I took the probability of getting a red, P(r)=26/52 and added it to the probability of getting a ten, P(10)=4/52 to get 30/52, but I forgot a step. 
My answer included the cards that were both red and 10. The question only asked for the chances of getting one or the other, not both. So you have to subtract the intersection: which is 2/52 because there are two cards that are both red and 10. So the real answer is 7/13 after you simplify. 
There were a couple questions that were similar to this question that confused me. I learned that when the question has 'or' in it, you need to subtract the intersection of both items. Also, I learned that to find the probability with an 'and' in the question you have to multiply the two item's probability to find the answer. For example; if you were to draw a card then return it to the deck and then draw again, what would be the probability that the first card is an ace and the second card is black? First, find the probability of drawing an ace: 4/52. Then find the probability of drawing a black card: 1/2. Now you add the two together and the the probability is 1/26!

This might sound a little confusing so here is an article about how to use a deck of cards for probability and examples to try. Click HERE to read it and try it out!