TSIA Prep - Probability

TSIA Prep - Probability

By Amy Davis

What is Probability on the TSIA?

Probabilistic and Statistical Reasoning includes:

• Classifying data

• Constructing appropriate representations of data

• Computing and interpreting probability

• Describing measures of center and spread of data

CollegeBoard TSIA2 Practice Test

Multiple Choice

The temperature at a location was recorded for 5 days. The median

temperature was 72 degrees. On four of the days, the temperatures were

67, 72, 77, and 52 degrees. Which of the following is not a possible

temperature for the fifth day?

• 80

• 70

• 79

• 83

List the numbers in order:

52, 67,​ 72, 77, ...

​

Median is the number in the middle. Since we have 5 days, that value is our third number.

​

In order​ for the median to be 72 as stated in the question, the fifth temperature must be greater than 72.

​

Therefore, 70 is not a possible temperature.​

Multiple Choice

Beth took a series of five math tests. Her average score on the first three

tests was 70. What must have been her average score on the last two

tests so that her overall average across all five tests was 80?

• 83.3

• 85

• 90

• 95

Multiple Choice

If two fair coins are tossed, what is the probability that both will come up

showing heads?

• 0

• $$\frac{1}{4}$$  

• $$\frac{1}{2}$$  

• 1

A single toss of a coin is an event that is not connected to or influenced by other events. When a coin is tossed twice, the coin has no memory of whether it came up heads or tails the first time, so the second toss of the coin is independent. The probability of heads on the first toss is 50%, just as it is on all subsequent tosses of the coin. The two outcomes of the toss of a coin are heads or tails.

​

A rule in probability states that the probability of the occurrence of two independent events is the product of their individual probabilities. Therefore, the probability of getting two heads on two coin tosses is 0.5 x 0.5 or 0.25.

Multiple Choice

Consider the set of numbers {3.5, 7, 12, 2.1, 1, 13.8, 4.2, 15, 8.9, 4.2}. If a

number is selected at random from this list, what is the probability that the

chosen number is less than the arithmetic mean of the numbers on the

list?

• 0.6

• 0.3

• 0.5

• 0.4

Multiple Choice

Daniel works for a market research firm. He has been assigned to conduct

a survey to find out if people like to watch movies at home or at the

theater. Accordingly, he conducted the survey by randomly picking

respondents outside a popular theater in his city and found that 172 out of

the 200 people surveyed said that they preferred visiting the theater.

Which of the following statements is a valid conclusion?

• It is likely that 86% of all residents who live around the theater where the survey was

  conducted prefer to watch movies at the theater rather than at home.

• It is likely that 86% of all residents of Daniel's city prefer to watch movies at the theater than

  at home

• Daniel's sample is biased and therefore his survey result is invalid.

• It is likely that 86% of all people in Daniel's country prefer to watch movies at the theater

  than at home