ACT Math : ACT Math
Study concepts, example questions & explanations for ACT Math
All ACT Math Resources
Example Questions
Example Question #4 : Outcomes
Two dice are rolled. What is the probability of getting two odd numbers on two dice?
1/2
1/8
2/3
1/4
1/6
1/4
Two independent events that each have a probability of 1/2 of occuring.
1/2 * 1/2 = 1/4
Example Question #1 : Probability
You are at the drawing for a raffle to win a new car. You bought 8 tickets for the raffle. If a total of 526 tickets were sold, what is the probability that your ticket is drawn?
0.022
0.008
0.0152
0.018
0.025
0.0152
Probability = # of Tickets You Bought / # of Tickets Sold
Probability = 8/526 = 0.0152
Example Question #5 : Outcomes
You roll a six sided die three times. What are the chances that all three rolls are 2?
1/216
1/6
1/12
1/36
1/18
1/216
Probability of each event = 1 side of die / # of sides = 1/6
Probability for multiple events = P1 * P2 * P3
1/6 x 1/6 x 1/6 = 1/216
Example Question #11 : How To Find The Probability Of An Outcome
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 #11 : 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 : How To Find The Probability Of An Outcome
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 #13 : How To Find The Probability Of An Outcome
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 #14 : How To Find The Probability Of An Outcome
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 #15 : 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 #131 : Data Analysis
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
Certified Tutor
All ACT Math Resources
