GED Math : Calculations
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Example Questions
Example Question #51 : Calculations
There are 12 marbles in a box. There are 5 blue, 2 green, 3 yellow, and 2 red. Two marbles are selected, WITH replacement. What is the probability of selecting one red and one yellow?
You can select red and yellow in one of two ways. That is 
It is key, in this problem, to recall that the selection is WITH replacement.
If we add the two probabilities, we get
Example Question #52 : Calculations
What is the probability of selecting a king from a deck of cards, putting it aside, and then selecting an ace?
This question involves probability WITHOUT replacement.
In a regular deck of cards, there are 52 cards, with 4 kings. The probability of selecting a king is 
The probability of selecting a kind AND an ace is
Example Question #51 : Calculations
Two regular 6-sided dice are thrown. What is the probability of rolling a sum of 8?
There are 36 equal outcomes when rolling two dice. The outcomes which fit the criteria of a "sum of 8" are 
The probability of rolling a sum of 8 is 
Example Question #54 : Calculations
How many different ice cream cones can be made using one of each of the following:
Flavor: Vanilla, Chocolate, Strawberry, Cookie Dough
Topping: Rainbow Sprinkles, Chocolate Sprinkles, Almonds, Chocolate Chips, Peanut Butter Cups
Cone Type: Waffle, Sugar
This question calls for the use of the counting principle. The counting principle has one multiply the number of options in each category. In this case, there are 4 options for flavors, 5 options for toppings, and 2 options for cone type.
So,
There are 40 different ice cream cones to be made using one in each category.
Example Question #55 : Calculations
On a movie and show night, a family plans on watching two shows and one movie. Consider the following:
1) The family has five shows that they really want to see, but decide that two will work.
2) After the shows, they will choose from one of seven DVD movies that they all agree on.
How many ways can the family watch two out of the five shows AND one of the seven movies on that night?
This employs the counting principle, much in the way one might be used to seeing.
The family has a combination of 2 out of the 5 shows AND 1 of the 7 movies.
We call the shows A, B, C, D, and E AND the movies 1,2,3,4,5,6, and 7.
1) Choosing two shows, we have {AB, AC, AD, AE, BC, BD, BE, CD, CE, DE}. The are 10 of these.
Choosing one movie, we have {1,2,3,4,5,6,7} There are 7 of these.
There are 10 "sets" of shows and 7 "sets" of movies.
Therefore, by the counting principle, the family has 10 x 7 options to choose from. There is a total of 70 options.
2) Another way is taking multiplying the combinations of shows and movies.
That is
Example Question #56 : Calculations
A weighted coin is flipped 
If the weighting is 
Example Question #52 : Calculations
Find the mean of the following numbers:
Example Question #53 : Calculations
Find the mean of the set of numbers below:
In this list,
Example Question #54 : Calculations
Given the data set 
I: The mean
II: The median
III: The mode
I, II, and III
I and III only
I and II only
II and III only
I, II, and III
The mean of a data set is the sum of its elements divided by the number of elements, which here is 8:
The median of a data set with an even number of elements is the mean of the middle two values when the set is arranged in ascending order; both of the middle elements are 8, so the median is 8.
The mode of a data set is the most frequently occurring element. Here, only 8 appears twice, so it is the mode.
All three are equal.
Example Question #3 : Mean
Veronica scored a 75 and a 71 on her first two exams. To raise her mean score to an 80, what grade does she need to earn on her third test?
94
85
80
73
90
94
The mean score is the sum of all scores divided by the number of scores.
First, find the sum of all three test scores, then divide by the number of tests, 3.
If Veronica wants her average to be 80, the equation becomes:
We need to solve for 
First, multiply both sides of the equation by 3:
Subtract 146 from both sides:
Veronica must score a 94 on her third test in order to bring her mean score to 80.
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