GED Math : Probability
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Example Question #51 : Probability
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 : Probability
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 : Statistics
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 : Probability
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 : Probability
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 #52 : Statistics
A weighted coin is flipped 
If the weighting is 
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