All GED Math Resources
Example Questions
Example Question #11 : Probability
A die is altered so that it comes up a "6" with probability . The other five outcomes are equally likely. If this die and a fair die are rolled, what is the probability that the outcome will be a total of "11"?
For a roll of "11" to occur with two dice, one die must show a "5" and the other must show a "6". In the fair die, "5" and "6" are two of six equally likely outcomes, so each will happen with probability .
In the loaded die, since a "6" will come up with probability , for the other five rolls to be equally likely, each, including "5", must come up with probability
.
The probability of rolling a "5" on the loaded die and a "6" on the fair die is
.
The probability of rolling a "6" on the loaded die and a "5" on the fair die is
.
Add these probabilities:
Example Question #12 : Statistics
A red die is altered so that it comes up a "6" with probability . The other five outcomes are equally likely. A blue die is altered similarly. If these two dice are rolled, what is the probability that the outcome will be a total of "2"?
For a "2" to be rolled with two dice, both dice must show a "1".
For each die, since a "6" will come up with probability , for the other five rolls to be equally likely, each, including "1", must come up with probability
.
The probability of a double "1" showing up will be
.
Example Question #13 : Statistics
A die is altered so that it comes up a "6" with probability . The other five outcomes are equally likely. If this die and a fair die are rolled, what is the probability that the outcome will be a total of "2"?
For a "2" to be rolled with two dice, both dice must show a "1". In the fair die, this is one of six equally likely outcomes, so it will happen with probability .
In the loaded die, since a "6" will come up with probability , for the other five rolls to be equally likely, each, including "1", must come up with probability
.
A double "1" will appear with probability
.
Example Question #11 : Probability
Roll a fair dice two times. What is the probability of NOT rolling a six on both trials?
A fair dice has 6 faces. Therefore, there is a sixth chance to land on any number between 1 through 6. Rolling the die the first time is independent from the second time, which means that we must account for the probabilities for each trial.
Probability of rolling a 6 is: 1/6
Since probability adds up to 1, the odds of rolling anything other than a 6 for one trial is:
1 - 1/6 = 5/6
On two trials:
Example Question #13 : Probability
Find the probability of drawing a red card from a deck of cards.
To find the probability of an event, we will use the following formula:
Given the event of drawing a red card from a deck of cards, we can calculate the following:
because there are 26 red cards in a deck
- 13 hearts
- 13 diamonds
Now, we can calculate the following:
because there are 52 total cards we could potentially draw.
So, we can substitute. We get
Therefore, the probability of drawing a red card from a deck of cards is .
Example Question #14 : Probability
A parking lot contains the following:
- 3 blue cars
- 2 white cars
- 4 black cars
Find the probability the next car that leaves is a blue car.
To find the probability of an event, we will use the following formula:
Now, given the event of a blue car leaves next, we can calculate the following:
because there are 3 blue cars in the lot.
We can also calculate the following:
because there are 9 total cars in the lot that could potentially leave:
- 3 blue cars
- 2 white cars
- 4 black cars
Now, we can substitute. We get
Example Question #15 : Probability
Find the probability of drawing a black card from a deck of cards.
To find the probability of an event, we will use the following formula:
So, given the event of drawing a black card from a deck of cards, we can calculate the following:
because there are 26 black cards in a deck
- 13 clubs
- 13 spades
Now, we can calculate the following:
because there are 52 total cards in a deck we could potentially draw. So, we can substitute. We get
Therefore, the probability of drawing a black card from a deck of cards is .
Example Question #12 : Probability
A bookshelf at the library contains the following:
- 10 chapter books
- 5 picture books
- 3 history books
Find the probability the next visitor selects a history book.
To find the probability of an event, we will use the following formula:
Now, given the event of selecting a history book, we can calculate the following:
because there are 3 history books on the shelf.
We can also calculate the following:
because there are 18 total books on the shelf we could potentially choose from:
- 10 chapter books
- 5 non-fiction books
- 3 history books
Now, we can substitute. We get
Therefore, the probability of selecting a history book is .
Example Question #13 : Probability
Find the probability of drawing a King, Queen, or Jack from a deck of cards.
To find the probability of an event, we will use the following formula:
Now, we will look at finding the probability of drawing a King, Queen, or Jack from a deck of cards. We will consider these as 3 separate events. We will find the probability of each, then add them together.
So, we will find the probability of drawing a King from a deck of cards. We get
because there are 4 Kings in a deck of cards:
- King of Hearts
- King of Diamonds
- King of Clubs
- King of Spades
We also get
because there are 52 cards in a deck that we would potentially draw.
So, we get
Now, we will do the same for finding the probability of drawing a Queen from a deck of cards.
because there are 4 Queens in a deck of cards:
- Queen of Hearts
- Queen of Diamonds
- Queen of Clubs
- Queen of Spades
We also get
because there are 52 cards in a deck that we would potentially draw.
So, we get
And lastly, we will find the probability of drawing a Jack. We get
because there are 4 Jacks in a deck of cards:
- Jack of Hearts
- Jack of Diamonds
- Jack of Clubs
- Jack of Spades
We also get
because there are 52 cards in a deck that we would potentially draw.
So, we get
Now, to find the probability of drawing a King, Queen, or Jack, we will add them all together. We get
Therefore, the probability of drawing a King, Queen, or Jack from a deck of cards is .
Example Question #21 : Probability
A card is selected from a standard deck of 52 cards. A student picks out a card, and does not replace the card. What is the probability that the student will pick out a club, and then another club?
The deck is divided into four suits: Clubs, Diamonds, Hearts, and Spades. There are 13 of each suit in a standard deck.
The probability of picking out a club out of a plain deck is:
The student does not replace the card back into the deck, which means that there are 51 cards remaining, and there are only 12 clubs remaining in the deck.
The probability of picking out another club would be:
To identity the probability, simply multiply the first and second probabilities.
The answer is:
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