Basic Probabilities

Basic Probability

Learning Objective: Students will determine the probability of an event.

Language Objective: Students will express their reasoning in written form.

Warm Ups

Order of Operations

When there is more than one math operation, use PEMDAS:

✓ Parentheses

✓ Exponents

✓ Multiplication and Division (from left to right)

✓ Addition and Subtraction (from left to right)

Example:Solve. (7 + 9) ÷ (32 ÷ 4) =

Multiple Choice

Evaluate the expression.

5 + (4 × 2) =

• 10

• 11

• 12

• 13

Multiple Choice

Evaluate each expression.

(12 − 5) − (4 × 3) =

• -5

• -3

• 5

• 9

Multiple Choice

Evaluate each expression.

(−9) + (12 × 6) + 15 =

• 17

• 33

• 78

• 432

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?

Multiple Choice

A bag contains two red marbles, three blue marbles, and four green

marbles. What is the sample space of the marble bag?

• red, blue, green

• 2, 3, 4

• 2 red, 3 blue, 4 green

• red, red, blue, blue, blue, green, green, green, green

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?

Multiple Choice

Linda is trying to pick out an outfit for school. She has 4 tops, 3 pants, and 5 shoes to pick from. How many total possible outfit combinations does she have?

• 3

• 5

• 12

• 60

Calculating Probability

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?

Multiple Choice

What is the probability of rolling an even number on a die?

• 0.25

• 0.5

• 0

• 1

Multiple Choice

In his Halloween bag, Jack got 3 Twix, 8 Snickers, 5 Lollipops, and 4 Reese’s. Jack pulls candy out of his bag at random. What is the probability of Jack pulling out a Twix or a Snickers on one try?

• $$\frac{11}{20}$$

• $$\frac{24}{20}$$

• $$\frac{11}{40}$$

• $$\frac{24}{400}$$

End of Lesson

Homework is due on Monday.