Probability & Counting – SAT, SHSAT & BCA Test Prep

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Einstein Circle

This lesson summary covers counting arrangements and basic probability. Included is a lesson on basic sequences and series. See the math toolbox for additional, focused video lessons and related exercises.

TestPrepSHSAT
Khan Academy
Math is Fun

TestPrepSHSAT

Sequences & Series

Probability & Combinations

Probability & Combinations

Welcome to the PROBABILITY/COMBINATIONS/PERMUTATIONS instruction unit.

These instructional quizzes are short, limited to only about a dozen questions, and they are not graded or timed. Occasionally there will be a question introducing a topic that you are not expected to answer at first. Do not panic. The instructional material will likely be introduced in the following answer explanation. The purpose of these instructional modules is to review subject material by topic that you will likely encounter on the exam and provide some topic specific tips to improve your ability to solve related problems.

DO YOU KNOW WHAT THE COUNTING PRINCIPLE IS FOR INDEPENDENT EVENTS?

Yes

No

Mary can drive or take a flight to NYC. From there she travels to Madrid and must choose from four available flights. Once in Madrid she can travel to her hotel by bus or taxi. How many different possible ways can Mary get to her hotel in Madrid?

Please enter the numeric value and not any variation. e.g. '8' and NOT "eight' or '2 cubed', etc.

There are 10 children in a class. How many ways can I line them up for recess?

$10$

$20$

$10!/2!$

$10!$

There are 10 students, 5 boys and 5 girls, in a class. How many ways can I line up the boys and girls for recess?

$10!$

$\frac{{10!}}{{5!}}$

$\frac{{10!}}{{5!5!}}$

$\frac{{10!}}{{2!}}$

$2$

There are 10 students in a class, 5 boys and 5 girls. How many ways can I sit them around a Harkness table?

$\frac{{10!}}{{5!5!}}$

$\frac{{9!}}{{5!5!}}$

$\frac{{9!}}{{5!4!}}$

$2 \times \frac{{9!}}{{5!4!}}$

How many ways can the letters in the word STATISTICS be arranged?

$\frac{{10!}}{{3!3!2!}}$

$\frac{{10!}}{{3!2!}}$

$\frac{{10!}}{{3!3!}}$

$\frac{{10!}}{{3!3!3!}}$

How many 3 digit numbers can be formed without repeating a digit?

(002, 091 and the like are not considered 3 digit numbers for this purpose)

252

648

900

999

There are 8 competitors for one event in the olympic games and only gold, silver, and bronze medals are awarded. How many possible combinations of medalists are there in this event?

8

56

144

336

What is the probability of rolling a 7 with two dice?

(any roll of a singular die can result in a number 1 through 6 and "rolling a 7" means the sum of the numbers facing upward on both dice equals 7)

16.7%

1/36

1/6

1/4

Do you think the chance of at least 2 students in your class having the same birthday is reasonably good or pretty low?

Pretty Low

Reasonably Good

What is the probability at least 2 students share a birthday in a class of 23 students?

<5%

5% up to, but not including 25%

25% up to, but not including 50%

>50%

Which of the following is true?

(check all that apply)

Count the possibilities of several independent events occurring by multiplying the possibilities of each event.

n unlike objects can be arranged n! ways.

If r objects are alike then divide by r! to avoid over-counting.

There are n!/(n-r)! ways to select r ordered objects from n total objects.

There are n!/r!(n-r)! ways to select r objects from n total objects where order doesn't matter.

Probability equals the number of ways an event can occur divided by the total possible outcomes,

Khan Academy

Khan Academy (Sequences, Series, Probability)

Arithmetic Sequences

Approximately 20 minutes in several videos.

Geometric Sequences

Approximately 15 minutes in several videos.

Probability

Approximately 10 minutes in several videos.

Venn Diagrams

Approximately 10 minutes in several videos.

Compound Probability

Approximately 15 minutes video.

Dependent Probability

Approximately 20 minutes in several videos.

Combinations

Approximately 10 minute video.

Permutations

Approximately 10 minute video.

Basic Set Operations

Approximately 10 minutes 1st two videos.

Math is Fun

Math Is Fun (Sequences, Series, Probability)

Sequences

Arithmetic Sequences

Geometric Sequences

Fibonacci Sequences

Infinite Series

Probability

Counting Principle

Probability Complement

Probability- Types of Events

Combinations & Permutations

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