ACT Math : Data Analysis
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Example Questions
Example Question #1 : Probability
A spinner has 3 equally distributed colors on it: blue, red, and yellow. There is an equal chance for the spinner to land on each color (1/3). What's the probability it will land on blue twice after 2 spins?
1/2
1/9
1/6
1/3
1/4
1/9
There are 9 possible ways for this outcome to be determined. They are contained in this set
{BB, BR, BY, RB, RR, RY, YB, YR, YY}.
Only one of these outcomes is desired, so the value is 1/9
Another way to solve this is to multiply the probability by the number of instances: thus two consecutive instances of "blue" will have the probability of one instance (1/3) multiplied by one instance (1/3), or 1/9.
Example Question #2831 : Act Math
Two dice are rolled. What is the probability of getting two odd numbers on two dice?
1/4
2/3
1/2
1/8
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 : How To Find The Probability Of An Outcome
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?
0.025
0.008
0.018
0.0152
0.022
0.0152
Probability = # of Tickets You Bought / # of Tickets Sold
Probability = 8/526 = 0.0152
Example Question #8 : Probability
You roll a six sided die three times. What are the chances that all three rolls are 2?
1/216
1/36
1/6
1/18
1/12
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 : Probability
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 #2832 : Act Math
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 #2833 : Act Math
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 : 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 #12 : Outcomes
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 #13 : Outcomes
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 
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