Probability review - Statistics and probability review

CliffsNotes CBEST - BTPS TESTING Ph.D., Jerry Bobrow Ph.D. & 8 more 2021

Probability review
Statistics and probability review

Life events are full of uncertainties, but inferential statistics can explain these events through the study of probability. The term probability is used in everyday life to predict the chance that a particular outcome will occur in a specific population or situation. For example, what is the probability that quarterback Patrick Mahomes will win another Super Bowl, or what is the probability that it will snow tomorrow? On the CBEST, the concept of probability is linked to the statistical confidence that a particular outcome may occur in real-life scenarios.

Measuring Probability

Probability problems are basically “ratio” problems and expressed as fractions. Probability is the numerical measure of the chance of an outcome or event occurring. When all outcomes are equally likely to occur, the probability of the occurrence of a given outcome can be found by using the following formula.

images

The probability, P, is expressed by dividing the number of desired outcomes by the number of possible outcomes.

Examples:

1.   What is the probability of throwing two dice in one toss so that they total 11?

A.  images

B.  images

C.  images

D.  images

E.  images

You can simply list all the possible combinations resulting in 11, (5 + 6 and 6 + 5), and realize that the total possibilities are 36, (6 × 6). Thus, the probability equals:

images

The correct answer is choice C.

2.   Two sixth-grade students are arguing about who was in line first to play tetherball. The teacher decides to toss a coin to settle the disagreement. The student who wins two out of three tosses is next to play. What is the probability of tossing a coin twice so that both times it lands heads up?

A.  images

B.  images

C.  images

D.  images

E.  images

The probability of getting a head in one throw is images. Because the teacher wants to throw a head twice, multiply the probability for the first toss images times the probability for the second toss images. Thus, images, and images is the probability of throwing heads twice in two tosses.

Another way of approaching this problem is to look at the total number of possible outcomes:

First Toss

Second Toss

H

H

H

T

T

H

T

T

There are four different possible outcomes and only one way to throw two heads in two tosses. Thus, the probability of throwing two heads in two tosses is 1 out of 4 total outcomes, or images. The correct answer is choice B.

Question 3 refers to the following graph.

3. In the spinner, all sections are equal. What is the probability of getting a blue on the first spin?

A. images

B. images

C. images

D. images

E. images

Because there are 3 favorable (blue) outcomes out of 8 total possible outcomes, the probability is images: images. The correct answer is choice C.

4. Corey charts the hair color of the students in her drama class. The chart gives the following information:

Hair Color

Number of Students

Black hair

12

Brown hair

18

Red hair

4

Blonde hair

6

5. From the information given in the preceding chart, if the teacher randomly picks a student to read a passage, what is the probability of the teacher selecting a student with black hair or red hair?

A. images

B. images

C. images

D. images

E. images

Because you’re looking for the probability of selecting a student with black hair or red hair to read a passage, you must first add:

images

Then get the total number of students in the class:

12 + 18 + 4 + 6 = 40

And finally set up the fraction images, which reduces to images. The correct answer is choice A.

5. Dexter is organizing his clothes to pack for a trip to New York. How many combinations of outfits are possible if he has 4 sports jackets, 5 shirts, and 3 pairs of slacks?

A. 4

B. 5

C. 12

D. 60

E. 120

Because each of the 4 sports jackets may be worn with 5 different shirts, there are 20 possible combinations. These 20 combinations may be worn with each of the 3 pairs of slacks for a total of 60 possible combinations. Stated simply, 4 × 5 × 3 = 60 possible combinations. The correct answer is choice D.