ACT Math : Data Analysis
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Example Questions
Example Question #12 : How To Find The Probability Of An Outcome
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 #12 : How To Find The Probability Of An Outcome
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 : Probability
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
3
27
24
9
27
Based on the chart there are three options in each category.
Total options = 3 * 3 * 3 = 27
Example Question #12 : 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 
Example Question #21 : Probability
There are 20 balls in a box, 10 are green, 5 are blue, and 5 are red. One red and one green ball are then removed from the box.
What is the probability that the third ball removed from the box will be green?
Not enough information given
This is a probability question, in the beginning, the odds of pulling a green ball were 10/20, which reduces down to 1/2. When 2 balls are removed, the total is now 18, and because there are only 9 green balls, we have a 9/18 chance of pulling a green ball, and this reduces down to 1/2
Example Question #22 : Probability
What is the probability that Jim flips a fair coin 3 times and gets 3 heads?
The probability of getting heads on one flip of a coin is 1/2, since the only other outcome is tails. Because the flips are independent of each other (one outcome does not depend on the others), the probability of the second coin being heads is 1/2 and the probability of the third coin being heads is 1/2. However, to calculate the probability of obtaining all of the flips ending in heads, we multiply the probabilities of the events together: (1/2)*(1/2)*(1/2) = 1/8.
Example Question #131 : Data Analysis
There is a box with 24 handkerchiefs, some are blue, some are red, and some are green.
If there are 4 red handkerchiefs in the box, and the probability of pulling a blue handkerchief is 3 times more likely than pulling a red one, what is the probability of pulling a green handkerchief?
If the probability of pulling out a blue handkerchief is 3 times that of pulling a red one, then it means there are 3 times as many blue handkerchiefs as there are red.
4 x 3 =12 blue handkerchiefs.
24 total – 12 blue – 4 red = 8 green handkerchiefs
8/24 simplifies into 1/3 (divide both numbers by 8)
Example Question #23 : Probability
There is a box with 24 handkerchiefs, some are blue, some are red, and some are green.
If there are 4 red handkerchiefs in the box, and the probability of pulling a blue handkerchief is 3 times more likely than pulling a red one, how many green handkerchiefs are in the box?
5
8
10
6
4
8
If the probability of pulling out a blue handkerchief is 3 times that of pulling a red one, then it means there are 3 times as many blue handkerchiefs as there are red.
4 x 3 =12 blue handkerchiefs.
24 total – 12 blue – 4 red = 8 green handkerchiefs
Example Question #23 : Probability
You roll two dice. The first die shows a 3 and the other die rolls under the table and you cannot see it. What is the probability that both die show 3 ?
1/3
1/6
9/36
5/6
1/36
1/6
A die has six sides and you already know that the first die shows the number 3. There is is a 1/6 probability that the second die under the table shows a 3.
Example Question #21 : How To Find The Probability Of An Outcome
Elena took a math test with 15 questions, each question having four choices. Elena is sure that she got exactly 9 of the first 12 questions correct, but she guessed randomly on the last 3 questions. What is the probability that she will get at least 80% on the test?
To get 80%, Elena needs to get 12 out of the 15 questions right. If she answered 9 out of the first 12 questions right, she can score 80% only if she guessed all 3 of the remaining questions correctly.
Therefore Elena has a (1/4)^3 chance of getting all 3 questions correct.
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