6, BECAUSE THERE IS ONE FAVOR-ABLE OUTCOME (ROLLING A 5) AND THERE ARE...
6
, because there is one favor-able outcome (rolling a 5) and there are 6 possible outcomes (rolling a 1, 2, 3, 4, 5, or 6). If an event is impos-sible, it cannot happen, the probability is 0. If an event definitely will happen, the probability is 1.C
OUNTING
P
RINCIPLE AND
T
REE
D
IAGRAMS
The sample spaceis a list of all possible outcomes. A tree diagramis a convenient way of showing the samplespace. Below is a tree diagram representing the sample space when a coin is tossed and a die is rolled.CoinDie OutcomesH112H23H3HH44H556H6T1T2T3TT4T5T6The first column shows that there are two possible outcomes when a coin is tossed, either heads or tails.The second column shows that once the coin is tossed, there are six possible outcomes when the die is rolled,numbers 1 through 6. The outcomes listed indicate that the possible outcomes are: getting a heads, thenrolling a 1; getting a heads, then rolling a 2; getting a heads, then rolling a 3; etc. This method allows you toclearly see all possible outcomes.Another method to find the number of possible outcomes is to use the counting principle. An exampleof this method is on the following page.–
A C T M AT H T E S T P R A C T I C E
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Nancy has 4 pairs of shoes, 5 pairs of pants, and 6 shirts. How many different outfits can shemake with these clothes?Shoes Pants Shirts4 choices 5 choices 6 choicesTo find the number of possible outfits, multiply the number of choices for each item.4 ×5 ×6 = 120She can make 120 different outfits.Helpful Hints about Probability
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If an event is certain to occur, the probability is 1.■
If an event is certain NOT to occur, the probability is 0.■
If you know the probability of all other events occurring, you can find the probability of the remainingevent by adding the known probabilities together and subtracting that sum from 1.M
EAN
, M
EDIAN
, M
ODE
,
AND
R
ANGE
Mean is the average. To find the mean, add up all the numbers and divide by the number of items.Median is the middle. To find the median, place all the numbers in order from least to greatest. Countto find the middle number in this list. Note that when there is an even number of numbers, there will be twomiddle numbers. To find the median, find the average of these two numbers.Mode is the most frequent or the number that shows up the most. If there is no number that appearsmore than once, there is no mode.The range is the difference between the highest and lowest number.Example
Using the data 4, 6, 7, 7, 8, 9, 13, find the mean, median, mode, and range.Mean: The sum of the numbers is 54. Since there are seven numbers, divide by 7 to find themean. 54 ÷ 7 = 7.71.Median: The data is already in order from least to greatest, so simply find the middle num-ber. 7 is the middle number.Mode: 7 appears the most often and is the mode.Range: 13 −4 = 9.L
INEAR
E
QUATIONS
An equation is solved by finding a number that is equal to an unknown variable.Simple Rules for Working with Equations