ACT Math : Probability
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Example Questions
Example Question #121 : Data Analysis
What is the probability of NOT getting a 7 when rolling two standard six-sided dice?
The sample space for rolling two six-sided dice is 36. We can get 7 six different ways: 1,6 2,5 3,4 4,3 5,2 6,1 so the probability of getting a 7 is 
Example Question #12 : Probability
Jack has a bag with 16 marbles in it. 8 white marbles, 6 green marbles, and 2 red marbles. Jack reaches into the bag and randomly chooses two marbles replacing each marble back in the bag after. What is the probability that he chooses 1 white marble with and 1 red marble?
The probability of choosing 1 white marble is 
The probability of choosing a red marble is 
To find the chances of both events happneing you must multiply the probabilities together.
Example Question #11 : Probability
If a marble is randomly chosen from a bag that contains exactly 12 purple marbles, 3 red marbles, and 10 blue marbles, what is the probability that the marble will NOT be blue?
To find the probability of a marble being chosen, we divide the number of the certain marble by the total number of marbles. In this case, we are finding the probability of NOT choosing a blue marble, or the probability of choosing a purple or red marble. The probability of choosing a purple marble is 
Example Question #11 : Probability
Suppose 30 percent of pet owners surveyed have both a cat and a dog, and 10 percent have neither. If there were twice as many pet owners who own only a dog as there were owners who only had a cat, what is the probability that a pet owner selected at random owns only a dog?
If 30% of owners have both a cat and a dog and 10% have neither, that leaves 60% of owners who either have only a cat or only a dog.
There are twice as many owners that only own a dog as owners that only own a cat. Thus, 
The total number of cat-only and dog-only owners make up 60% of those surveyed. Thus,
Substitute 
Solve for 
Plug answer into first equation to get value of 
Example Question #11 : Probability
What is the probability of not getting an even number less than six when rolling two six-sided dice?
The sample space for rolling two six-sided dice is 
Even numbers less than 6 are 4 and 2:
So the probability of getting an even number less than six is
So the probabilty of not getting an even number less than six is
Example Question #12 : How To Find The Probability Of An Outcome
There are 20 people going to a company party. One person is chosen at random to bring the cake. However, no one can bring a cake two parties in a row. Assuming the same 20 people go to every company party, what is the probability that Leslie, who did not bring the cake last time, will be chosen?
This is a probability question. All you have to account for is that one of the twenty people at this party brought a cake last time so they will not need to bring it this time. Therefore we take one person away from the twenty leaving nineteen people. Leslie has a 
Example Question #17 : Probability
Given a standard deck of 52 playing cards, where half (clubs and spades) are black and half (hearts and diamonds) are red, what is the probability of picking three black cards in a row if the cards are not replaced?
Probability that first card is black:
Now there are 25 black cards remaining in the deck.
Probability that second card is black:
Now there are 24 black cards remaining in the deck.
Probability that third card is black:
The probability of getting three black cards in a row is
Example Question #18 : Probability
A bag of colored candies contains 37 pieces: 5 red, 12 purple, 7 orange, 3 green and 10 yellow. Wanda eats 1 of each. What is the probability that the next piece she chooses will be orange?
There are 5 colors of candy, so if she eats one of each there are now 32 pieces remaining, 6 of which are orange. The probability of grabbing an orange piece is then 
Example Question #11 : How To Find The Probability Of An Outcome
Each student must choose one sport, one fine art and one club to be involved in. If the chart above shows all the possibilities available, how many different combinations of activities are possible?
15
24
3
9
27
27
Based on the chart there are three options in each category.
Total options = 3 * 3 * 3 = 27
Example Question #11 : Probability
A fair die is rolled three times. What are the odds that the die will come up a six on all three rolls?
The probability the die will turn up six on any given roll is 
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