SOLUTION: What is the probability of drawing a 5 or a diamond from a standard deck of cards?

Hi, there--

PROBLEM:
What is the probability of drawing a 5 or a diamond from a standard deck of cards?

A SOLUTION:
The probability of a particular event occurring is  "the number of ways that event can happen"
divided by "the number of all possible events that can occur" in the sample space.

There are 4 ways to draw a 5 because there are four 5s in a standard deck of cards.
There are 13 ways to draw a diamond because there are 13 diamonds in the deck.
There are 52 ways to draw any card from the deck because... (You get the idea.)

LET A be the event of drawing a 5
P(A) = the probability of drawing a 5  = 4/52

LET B be the event of drawing a diamond
P(B) = the probability of drawing a diamond = 13/52

You want to know the probability of drawing a 5 OR a diamond. 

First you need to decide if these two events are mutually exclusive or not. Is it possible to 
draw a 5 AND a diamond in a single turn? 

Yes, there is one way (if you draw the 5 of diamonds.) So
P(A AND B) = 1/52

To find the probability of A OR B occurring, we add the probabilities together.

P(A) + P(B) = 4/52 + 13/52 = 17/52

Now we need to subtract the probability of drawing a 5 AND a diamond to that we don't 
double count the 5 of diamonds. (It's in the "ways to draw a 5" list and the "ways to draw 
a diamond" list.

P(A or B) = P(A) +P(B) - P(A and B) = 4/52 + 13/52 - 1/52 = 16/52 = 4/13

That's it. Calculating probabilities can be complicated until you get the hang of it. Feel free to 
email if you have questions about this explanation.

Mrs.Figgy
math.in.the.vortex@gmail.com