probability (ioline)

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

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?

• $$\frac{11}{20}$$

• $$\frac{24}{20}$$

• $$\frac{11}{40}$$

• $$\frac{24}{400}$$

Multiple Choice

Twenty students are selected at random from a group of 500 students that took a common test. Of those twenty, six students received an A on the test.

Based on the given, if a student from the entire group is picked at random, what is the probability that he or she scored a grade lower than A?

• 7/10

• 7/20

• 2/5

• 3/10

Multiple Choice

What is 2% of 50?

• .25

• .50

• 1

• 2

Multiple Choice

12% of what number is 48?

• .50

• .84

• 4

• 400

Vocabulary

A compound probability is a probability involving two or more events, for example, the probability of Event A and Event B happening.

For example the compound probability may be like the following:

A. What’s the probability of flipping a coin twice and having it come up heads both times?

B. P(Comes up heads) =

C. P(1^st flip comes up heads AND 2^nd flip comes up heads) =

Vocabulary

Independent Probability: The outcome of one event does not effect the outcome of the other event. *Look for words like: replace, replacement, put back*

Example: Rolling a six-sided die and spinning a spinner.

Vocabulary

Dependent Probability: The outcome of one event affects the outcome of the other event. *Look for words like: without replacement, at the same time, or one afer another.*

Example: Suppose two M&M’s are drawn from the bag above. The first M&M is not replaced before the second M&M is drawn.  

Example 1

Tell whether the events are dependent or independent.

A) One tossed coin landing heads and the next landing tails.

B) Drawing two cards from a deck of cards at the same time.

Multiple Choice

Tell whether the events are dependent or independent.

Rolling two sixes in a row on a number cube.

• Independent

• Dependent

Formula: Independent Event (with replacement)

Multiple Choice

A bag contains 4 blue marbles, 6 green marbles and 3 yellow marbles. If two marbles are drawn at random from the bag.

What’s the probability of drawing a green marble, replacing it, and then drawing a yellow marble?

• 
  

  $$\frac{9}{13}$$

• $$\frac{54}{13}$$

• $$\frac{9}{169}$$

• $$\frac{18}{169}$$

Formula: Dependent Event (without replacement)

Multiple Choice

A bag contains 4 blue marbles, 6 green marbles and 3 yellow marbles. If two marbles are drawn at random from the bag.

What’s the probability of drawing a green marble, without replacing it, and then drawing a yellow marble?

• $$\frac{3}{25}$$

• $$\frac{9}{25}$$

• $$\frac{3}{26}$$

• $$\frac{9}{26}$$