Probability 2(IOLINE)

Probability

Permutations and Combinations

Permutations

Combinations

What's the difference?

• The order of the elements

For Example...

• In permutations, we care about the order

• AB is not the same as BA

• In combinations, the order doesn't matter

• AB is the same as BA

Vocabulary

Probability: the likelihood of something happening. It is expressed as a number between 0 (will never happen) and 1 (will always happen). It can be expressed as a decimal, fraction, percentage or ratio.

Vocabulary

Experiment: a situation involving chance that leads to the result called the outcome.

Outcomes: the result of a single trial of an experiment.

Event: one or more outcomes of an experiment.

Sample Space: the set of all possible outcomes of that experiment.

Examples

Example 1: What is the sample space for choosing a prime number less than 15 at random?

Example 2: What is the sample space for choosing 1 jelly bean at random from a jar containing 5 red, 7 blue, and 2 green jelly beans?

Example 3: What is the sample space for choosing 1 letter at random from the word DIVIDE?

Fundamental Counting Principle

States that if event x can occur in x ways and event y can occur in y ways, then x followed by y can occur in x×y ways. Or in other words, to find the total outcomes possible you take the total outcome from the first event and you multiply it by the total outcome of the second event.

Example 4

The cafeteria has 4 types of sandwiches, 6 types of chips and two types of drinks. How many possible lunch combos are there?

Calculating Probability

Formula:

Example 5

A bag contains 4 blue marbles, 6 green marbles and 3 yellow marbles. A marble is drawn at random from the bag.

a) What is the probability of drawing a green marble?

b) What is the probability of drawing a yellow marble?

c) What is the probability of drawing a blue marble?

d) What is the probability of drawing a red marble?

What is Factorial?

• Factorials (!) are products of every whole number from 1 to n.

• If n is a positive integer, n factorial is denoted by n! is a product of all positive integers less than or equal to n.

• It is defined by: n! = n(n - 1)(n - 2) . . . (2) (1)

• It’s a shorthand way of writing numbers. 

What is Factorial?

• As a SPECIAL CASE:

• 0! = 1