ACT Math : Data Analysis

Study concepts, example questions & explanations for ACT Math

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Example Questions

Example Question #63 : Probability

When rolling a ten sided die, what is the probability you roll an even number? Leave your answer as a reduced fraction.

Possible Answers:

Correct answer:

Explanation:

To find the probability find the total number of ways to get the described event (rolling an even number: 2,4,6,8,10 for a total of 5) divided by the total number of outcomes (10). Thus the answer is:

.

Remember to reduce the fraction!

Example Question #64 : Probability

If you draw a single card from a standard deck of cards, what is the probability that you draw a face-card that is also a diamond (face-cards do not include )?

Possible Answers:

Correct answer:

Explanation:

To find the probability of an event, find the total number of ways the event can happen and divide that by the total number of outcomes. There are only  face-card diamonds (King, Queen, Jack), and there are 52 possible cards to draw. Thus:

Example Question #64 : Probability

Ilene has a bag of gum drops and a bag of gummy bears.  The bag of gum drops contains 23 gum drops in the following colors: 3 red, 3 orange, 4 brown, 4 green, 6 blue and 3 yellow.  The bag of gummy bears contains 26 gummy bears in the following colors: 4 red, 6 orange, 5 purple, 3 green, 5 yellow and 3 pink.  If she dumps all of the gum drops and gummy bears into one bag, what is the probability that she will pick up either a red or green gum drop or gummy bear?

Possible Answers:

7/14

3/49

2/7

1/7

2/47

Correct answer:

2/7

Explanation:

The total number of gum drops and gummy bears is 49.  There are 7 red gum drops and gummy bears and 7 green gum drops and gummy bears.  There is a 2 in 7 probability that you will pick up a green or red gum drop or gummy bear.

If you answered 1/7, then you only accounted for choosing either red gum drop or gummy bear or green ones. 

If you answered 2/47 then you did not add the number of gum drops and gummy bears correctly.

If you answered 7 in 14 then you found the number of red or green gummy bears/gum drops out of the total red and green gummy bears and gum drops. 

And if you answered 3 out of 49, you found only the probability of choosing either red gum drops or green gummy bears. 

Example Question #181 : Data Analysis

Kaleah was born on the 17th day of the month. What is the probability that the next person she meets was born the 17th day of the month if they were born in August?

Possible Answers:

Correct answer:

Explanation:

To find the probability of an event, find the number of ways that even can happen divided by the total number of possible outcomes.

There are 31 days in August, thus the total number of outcomes for someone being born in August is 31.

Since we only care about the event that is being born on the 17th, there is only one way that event can happen (being born on August 17th).

Thus the probability is 

.

Example Question #71 : How To Find The Probability Of An Outcome

When drawing a single card from a deck of cards, what is the probability you draw a black card, or a two? Give your answer as a simplified fraction.

Possible Answers:

Correct answer:

Explanation:

To find the probability of an outcome, find the total number of ways that event can happen divided by the total number of possible outcomes.

There are 52 cards in a deck of cards, so there are 52 total possible outcomes. Of those, there are 26 black cards, and 4 twos.

However, of those 4 twos, two have already been included when we counted the 26 black cards (the 2 of clubs and 2 of spades), thus there are only two additional twos to add to our total of 26 black cards.

This yields 28 possibilities, which when divided by 52 reduces to:

Example Question #183 : Data Analysis

What is the probability of drawing a face card from a standard, 52 card deck of cards? Give your answer as a reduced fraction.

Possible Answers:

Correct answer:

Explanation:

To find the probability of an event, determine the number of ways the event can happen, and divide that by the total number of possible outcomes.

Because there are 52 cards in a deck of cards, the total possible number of outcomes is 52.

Since there are 3 face cards (Jack, Queen, King) and four suits, there are a total of 12 face cards.

Example Question #73 : How To Find The Probability Of An Outcome

When rolling at  die, what is the probability that you roll a number greater than ? Give your answer as a reduced fraction.

Possible Answers:

Correct answer:

Explanation:

To find the probability of an outcome figure out the number of ways the specified event can occur (rolling a number greater than ), divided by the total number of outcomes. Since there are  possible numbers to roll, the total number of outcomes is . The numbers greater than  are:  for a total of  possibilities. Thus the answer is:

.
(Note,  is not included in "greater than", if it said "greater than or equal to " it would be).

Example Question #2893 : Act Math

When rolling a  die, what is the probability you roll a number less than or equal to ? Give your answer as a reduced fraction.

Possible Answers:

Correct answer:

Explanation:

To find the probability of an event, find out how many ways that specific event can happen and divide it by the total number of possible outcomes. The only numbers less than or equal to  on a  sided die are  and . There are  possible outcomes. Thus the reduced fraction is: 

Example Question #71 : How To Find The Probability Of An Outcome

Aaron flips a fair coin 7 times. The outcomes are shown below, in the order of the coin flips. H denotes heads, T denotes tails. Which outcome is most unlikely?

 

I)  HHHHHHH

II) TTTTTTH

III)THHTHTT

Possible Answers:

I and II

I

They are equally unlikely.

II

III

Correct answer:

They are equally unlikely.

Explanation:

Even though I and II may seem like rarer outcomes, all of the answer choices have an equal probability of occurring, as the probability for each outcome is 0.50 in each flip and the probability for each of these sequences of coin flips equals (0.50)^7.

Example Question #71 : Probability

If you roll a six-sided die, what is the probability of rolling a prime number?

Possible Answers:

Correct answer:

Explanation:

 are the prime numbers on a die, so since there are 6 sides the odds would be .

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