SAT Math : How to find the probability of an outcome

Study concepts, example questions & explanations for SAT Math

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Example Questions

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Example Question #141 : Probability

The given table reports the average high and low temperatures over four years. What is the average rate of change for the high temperature during the four years?

Note: The temperature is in degrees Fahrenheit.  

Possible Answers:

Correct answer:

Explanation:

The given table reports the average high and low temperatures over four years. The question asks to calculate the average rate of change for the high temperature over the four years depicted.

To calculate average rate of change use the following formula.

Substitute these values into the formula looks as follows.

Therefore, the average rate of change for the high temperature from 2002 to 2005 is 2 degrees Fahrenheit.

Example Question #142 : Probability

The given table reports the average high and low temperatures over four years. What is the fraction of average low temperatures in 2002 to 2005?

Note: The temperature is in degrees Fahrenheit.  

Possible Answers:

Correct answer:

Explanation:

The table reports the average high and low temperatures over four years. To calculate the fraction of average low temperatures in 2002 to 2005 first identify the average low temperature in 2002 and in 2005.

Examining the table,

Average low temperature in 2002: 34 degrees Fahrenheit.

Average low temperature in 2005: 45 degrees Fahrenheit.

From here, to find the fraction of average low temperatures during this time period, use the following formula.

Example Question #143 : Probability

A poll was taken from a random collection of  people, they were asked whether they approve or disapprove GMO's. 

 

 

 

Did GMO's have a higher approval rate in September or October?

Possible Answers:

October

September

Correct answer:

October

Explanation:

To figure out which month had a higher approval rate, we need to divide the approve number by the total number of people.

From this, we can determine that October had the highest approval rate.

Example Question #144 : Probability

Below is a table of earnings from playing blackjack.

 

Find the rate at which this is depreciating at each month.

Possible Answers:

Correct answer:

Explanation:

To determine what the rate is, we need to divide the proceeding value by the preceding value, for instance.

If we do this for the rest of the values, we will get the common ratio of .

 

Example Question #145 : Probability

 

The above table shows how many people participated in a sport at a local gym. What is the probability that a man played basketball?

Possible Answers:

Correct answer:

Explanation:

In order to solve this, we need to look at the table. We simply take the number of men that played basketball and divide it by the total in the men row. 

Example Question #146 : Probability

A research study was conducted where 300 participants were selected at random. Half received Treatment X and half did not. Those that received Treatment X had significantly improved eyesight. Based on the design and results of the study, which is an appropriate conclusion?

Possible Answers:

Treatment X is better than other treatments, will improve the eyesight of anyone

Treatment X is less likely to improve the eyesight of people who have poor eyesight

Treatment X is likely to improve the eyesight of people who have poor eyesight

Treatment X is worse than other treatments, and will not improve the eyesight of anyone

Correct answer:

Treatment X is likely to improve the eyesight of people who have poor eyesight

Explanation:

The best answer is ,"Treatment X is likely to improve the eyesight of people who have poor eyesight" because Treatment X is likely to improve eyesight, and the participates had poor eyesight to begin with.

Example Question #141 : Probability

Spinner

The image above represents a spinner with 10 regions.  The 6 larger sectors have a radius that is twice that of the smaller sectors.

If spun, what is the probability that the spinner will stop while pointing to a green sector?

Possible Answers:

Correct answer:

Explanation:

The probability that the spinner will stop in a particular sector depends on the angle of the sector, not on the size of the sector. The radii of the sectors is therefore irrelevant.

The two larger green sectors are each one third of a quarter circle, and each is a sector of measure

.

The two smaller ones are each a half of a quarter circle, and each is a sector of measure 

.

Therefore, the total angle measure of the green sectors is

.

The probability that the spinner will stop in a green sector is found by taking this out of a total of :

Example Question #311 : Data Analysis

 

The above table shows how many people participated in a sport at a local gym. What is the probability that someone swam?

Possible Answers:

Correct answer:

Explanation:

To figure out this probability, we will take the total number of people under swimming and divide by the total number of people.

Example Question #2 : How To Find The Probability Of An Outcome

You have a full deck of 52 cards.  If there are four queens in the deck, what is the probability that out of two cards dealt to you both are queens?

Possible Answers:

0.0045

0.0052

0.0049

0.0033

0.0048

Correct answer:

0.0045

Explanation:

Probability of each event = (# queens)/ Total # of cards

P1 = 4 / 52

Second event assumes a queen  was chosen for first event so there is one less queen and also one less card:

P2 = 3 / 51

Probability for multiple events = P1 x P2

(4 / 52) * (3 / 51)

( 4 * 3) / (52 * 51 ) = 12 / 2652 = 0.0045

Example Question #149 : Probability

A lottery is being run at a high school to allocate parking spots.   The school has 200 seniors, 300 juniors, 350 sophomores, and 450 freshmen.  Each eligible senior will have their name entereted into the lottery twice, with all other eligible students' names being entered once.  Only juniors and seniors will be eligible for parking spots.  If there are 150 parking spots, what is the probability that any given junior will receive a spot?

Possible Answers:

3/14

1/100

2/7

4/9

3/5

Correct answer:

3/14

Explanation:

Find the probabilty a junior's name will be pulled for a single lottery trial.  Then calculate the probability given 150 lottery trials.

(200 seniors * 2 entries each) + 300 juniors = 700 entries

For any single junior then, the odds are 1/700 for a single lottery trial.

For 150 trials, a junior will have (1/700 * 150 trials) = 150/700, which simplifies to

3/14 

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