PSAT/NMSQT Prep 2022 - Eggert M.D., Strelka A. 2022

Probability
Tables, statistics, and probability
Data analysis

LEARNING OBJECTIVE

After this lesson, you will be able to:

· Calculate probabilities based on data sets

To answer a question like this:

Levels Passed in Video Game

The above table shows how many levels each player passed in the same video game. If these players represent a random sample, what is the probability that a given player will pass at least four levels in this game?

A. 25%

B. 33%

C. 50%

D. 67%

You need to know this:

Probability is a fraction or decimal between 0 and 1 comparing the number of desired outcomes to the number of total possible outcomes. A probability of 0 means that an event will not occur; a probability of 1 means that it definitely will occur. The formula is as follows:

For instance, if you roll a six-sided die, each side showing a different number from 1 to 6, the probability of rolling a number higher than 4 is , because there are two numbers higher than 4 (5 and 6) and six numbers total (1, 2, 3, 4, 5, and 6).

To find the probability that an event will not happen, subtract the probability that the event will happen from 1. Continuing the previous example, the probability of not rolling a number higher than 4 would be:

The PSAT tends to test probability in the context of data tables. Using a table, you can find the probability that a randomly selected data value (be it a person, object, etc.) will fit a certain profile. For example, the following table summarizing a survey on water preference might be followed by a question asking for the probability that a person randomly selected for a follow-up survey falls into a given category.

If the question asked for the probability of randomly selecting an urbanite who prefers tap water from all the participants of the original survey, you would calculate it using the same general formula as before:

If the question asked for the probability of randomly selecting an urbanite for the follow-up survey, given that the chosen participant prefers tap water, the setup is a little different. This time, the number of possible outcomes is the total participants who prefer tap water, which is 629, not the grand total of 1,690. The ­calculation is now:

Conversely, if you needed to find the probability of selecting someone who prefers tap water for the follow-up survey, given that the chosen participant is from an urban area, the new number of possible outcomes would be the urban participant total (887). The calculation becomes:

You need to do this:

· Determine the number of desired and total possible outcomes by looking at the table.

· Read the question carefully when determining the number of possible outcomes: do you need the entire set or a subset?

Explanation:

Use the probability formula: . The numerator is the number of people who can pass at least four levels, which is 4. The total number of people in the data table are 6. So, . The closest answer to this is (D).

Try on Your Own

Directions: Take as much time as you need on these questions. Work carefully and methodically. There will be an opportunity for timed practice at the end of the chapter.

18. Frankie, Bao, Craig, and Ekanta are selling boxes of fruit to raise money for a senior class trip. The summary of their sales is provided in the table above. The students decide to give away a free box of fruit to someone who purchased from them. Assuming no buyers purchased more than one box of fruit, what is the probability that the randomly selected buyer had previously purchased a box of berries or exotic fruit?

Questions 19 and 20 refer to the following information.

The table above shows the number of apples, bananas, oranges, and pineapples sold at Freddie’s Fruit Stand during each of the four seasons in 2018.

19. Of the following, which is closest to the percentage of all the pieces of fruit sold that were bananas?

A. 15%

B.20%

C.24%

D. 30%

HINT: See if you can answer Q20 without actually calculating exactly what percentage of fruit sold is pineapples.

20. For which season did pineapples make up the largest percentage of the total pieces of fruit sold?

A. Winter

B.Spring

C.Summer

D. Fall

21. Students at Fairview High School were asked to rate their level of agreement with the school’s decision to change the school colors from blue and white to maroon and orange. The results are shown in the table above, by level of agreement and class of student. If underclassmen are defined as freshmen and sophomores, what percentage of underclassmen agree or strongly agree with the new policy? Round your answer to the nearest whole number and ignore the percent sign when gridding your response.

HINT: Take the time to make sure you’re pulling the correct information from the table and graph for Q22.

Table 1

A large fruit orchard has 2,500 orange trees. Table 1 above shows the distribution of ages of the orange trees in the orchard. A county inspector has been notified that a highly contagious bacterial disease called citrus canker has infected some of the orange trees. The inspector randomly tests 4% of each age group of the trees. Her findings are shown in Table 2 below.

Table 2

22. What is the probability that an orange tree selected at random from the tested trees less than 3 years old will have citrus canker?

A. 0.03

B.0.12

C.0.15

D. 0.53