Probability Basics

Probability Basics

Objective: Find the probability of simple events.

​Probability: refers to the likelihood of an event or combination of events occurring.

​Probabilities can fall anywhere from 0 to 1.

0 means the event will never occur.

1 means the event will always occur.

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A probability between 0 and 1 means the event will sometimes occur; the higher the value, the greater the likelihood of the event.

​Probability Formulas

​Converting

​Example

Multiple Choice

The numbers 4 through 14 are placed in a bowl and drawn at random then replaced after being drawn. What is the probability of drawing a 9?

• 9%

• 10%

• 0.9%

• 0.01%

• 0.09%

Multiple Choice

Which shape has a 35% chance of being selected?

• heart

• diamond

• circle

​Independent Events

If the first event DOES NOT influence the second, we can use the following formula.

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Probability of Two Independent Events =

Probability of 1st Event × Probability of 2nd Event

​EXAMPLE (long way)

​Consider a game where you first flip a coin and then roll a die. How might we determine the probability of first flipping “heads” then rolling either a 5 or 6?

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​​Maybe create a tree diagram:

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​Number of Successful Outcomes =

Number of Possible Outcomes =

​EXAMPLE (short way)

​Consider a game where you first flip a coin and then roll a die. How might we determine the probability of first flipping “heads” then rolling either a 5 or 6?

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​​Probability of Two Independent Events =

Probability of 1st Event × Probability of 2nd Event

Multiple Choice

You roll a die and then flip a coin. What is the probability, as a percent, of getting an even number on the die and then a head on the coin?

• 25%

• 30%

• 10%

• 50%

Multiple Choice

A spinner is pictured.

If you spun the spinner two times, what is the probability of landing on a white space and then a light gray space?

• 5%

• 50%

• 10%

• 0.05%

• 0.01%

​Dependent Events

If the first event DOES influence the second, we can use the following formula.

​

Probability of Two Dependent Events =

Probability of 1st Event × Probability of 2nd Event after the first event

​Example

There are eight shirts in your closet, four blue and four green. You randomly select one to wear on Monday and then a different one on Tuesday. What is the probability you wear blue shirts both days?

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Probability of Two Dependent Events =

Probability of 1st Event × Probability of 2nd Event after the first event

Multiple Choice

Shareen has to select two students from a class of 23 girls and 25 boys. What is the probability that both students chosen are boys?

• 27%

• 26%

• 25%

• 48%