# Probability

### Description:

Probability questions test your knowledge of the basic rules of probability. Difficult questions may ask you to calculate a combination or a permutation for a given scenario.

#### Approach:

Basic probability rules must be memorized. Use your calculator to determine the answer to a difficult combination (nCr) or permutation (nPr) question.

#### 1) Basic Probability

To determine the probability of an event you must determine the number of possible outcomes and the number of desired outcomes.

Probability of Event = Desired Outcomes / Total Outcomes

Thus the probability of rolling a 3 on a 6 sided die is: 16

#### 2) Probability of one event or another

"Or" is treated as addition in probability because either of the two events can occur.

Probability of Event A or B = Probability of Event A + Probability of Event B.

Thus the probability of rolling a 3 or a 4 is: 16 + 16 = 13

#### 3) Probability of one event and another

"And" is treated as multiplication in probability because both events have to occur.

Probability of Event A and B = Probability of Event A * Probability of Event B.

Thus the probability of rolling two 3s in a row is: 16 * 16 = 136

#### 4) Quick Probability

OR AND
One event OR another event One event AND another event
ADD the two probabilities MULTIPLY the two probabilities

#### 5) Permutations (nPr)

Look for the words ORDER or ARRANGEMENT to know you need a permutation. A permutation refers to the number of different orders in which a set of elements can be arranged. For instance, if John and Suzie are standing in a line, there are only two permutations (orders) possible. John can be first and Suzie second, or the other way around.

For example, to determine how many ways that 5 people could be arranged into 4 seats, you would enter 5 nPr 4 into your calculator. Or you can diagram permutation problems by drawing places for the elements involved and filling in the number of options available at each space.

For the problem above you would have four spaces with 5, 4, 3, and 2 entered into them. After you have filled in the spaces multiply 5 * 4 * 3 * 2 = 120

Permutation equation: nPr = n!(n - r)!

#### 6) Combination (nCr)

Look for the word GROUP to know you need a combination. In combination problems, order does not matter. Common combination situations include choosing ingredients for a stew or choosing people to participate in a game (in which order of participation does not matter).

For example, if you wanted to determine how many ways that 2 people could be chosen for student council from a class of 10, you would enter 10 nCr 2 into your calculator. Or you can diagram combination problems by drawing places for the elements involved and filling in the number of options available at each space. However, unlike with permutations, combination problems do not involve order so you have to divide the result by the number of ways you can arrange the elements.

For the problem above you would have two spaces with 10 and 9 entered into them. After you have filled in the spaces multiply 10 * 9 = 90. Finally, divide by 2 * 1 to remove the order from the answer.

Combination equation: nCr = n!(r!(n - r)!)

#### 7) Calculator Instructions

PERMUTATION COMBINATION
1. Enter number of elements (people, ingredients, etc.) 1. Enter number of elements (people, ingredients, etc.)
2. Press MATH; select PRB; select nPr 2. Press MATH; select PRB; select nCr
3. Enter number of spaces available 3. Enter number of spaces available

#### 8) Practice:

• If five people are getting into a car and only two of the five people can drive, how many ways can you arrange the people in the car? (permutation: 48)
• You need to select two plumbers from a list of ten, how many combinations of plumbers are possible? (combination: 45)
• You are asked to create a password using only letters and without repeating any letter. How many 4 letter passwords are possible? (permutation: 358800)