Probability of Compound Events 

Compound probability is the probability of two or more simple events.  Example of Independent Compound Event:  Find the probability of rolling a 6 on a number cube and getting a head on a coin toss.  Since the probability of rolling a six is 1/6 and the probability of getting a head on a coin toss is 1/2, then the probability of rolling a 6 and getting a head is 1/6 times 1/2, which is equal to 1/12.  The rule is simply to multiply the probabilities of each simple event.    Example of a Dependent Compound Event:  If a compound event is "dependent," then the second event depends on the first event.Find the probability of picking a yellow marble and then a green marble from a jar containing 4 yellow marbles and 5 green marbles if the first marble is not replaced. Solution:  P(yellow) = 4/9 and P(green) = 5/8 (There are still five green marbles, but there are only eight total marbles because one of the yellow marbles was taken on the first draw.)  Take the two probabilities and multiply:  4/9 times 5/8 = 20/72 = 5/18

Experimental and Theoretical Probability

Theoretical probability is based on what is expected.  The theoretical probability of rolling a 2 or 3 on a number cube is 2/6 = 1/3.  There are two favorable choices out of 6 possible outcomes.   If asked for the experimental probability of rolling a 2 or 3, it would be based on the experiment, or what actually happens.  For example, if one rolled a number cube 20 times and it landed on a two 4 times and a three 5 times, then the experimental probability would be 9/20.      

Discount

Discount refers to how much is being deducted from the original price.  For example, if the discount is 25% on an item that costs $10.00, then you would only pay $7.50. For this example, the discount is calculated by taking the original cost $10.00 and multiplying by 0.25 (the amount of the discount written as a decimal).  This would give you the discount amount of $2.50.  Then, you would have to take the original price of $10.00 and subtract the $2.50 to get the sale price of $7.50. The other method, or shortcut method, is to calculate the sale price without actually calculating the amount of the discount first.   If an item is discounted 25%, then you are actually paying the other 75%.  Therefore, if the original price is $30.00, you would actually only be paying 75% OF the original cost.  So, $30.00 x 0.75 = $22.50.   

Percent of Discount

Finding the percent of discount is done when you know the sale price and the original price.  The easiest way is to write a ratio (fraction), convert it to a decimal, and then to a percent.  For example, suppose an item is on sale for 16.00 and the original price was $24.00.  The discount is $8.00 off the original price.  So, write 8/24 (8 divided by 24), which is .33333... , then change the decimal to a percent (Dr. Pepper), which is 33 1/3%.   Another method is to set up a proportion 8/24 = x/100.  When you solve for x, that will be the percent of the discount.