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.

​

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

Fill in the Blanks

A jar contains 12 caramels, 7 mints, and 16 dark chocolates. What is the probability of selecting a mint expressed as a fraction?

**NOTE: you HAVE to SIMPLIFY the fraction**

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%

Fill in the Blanks

You roll a single die numbered from 1 to 6. What is the probability of rolling an odd number, expressed as a fraction?

**NOTE: you HAVE to SIMPLIFY the fraction**

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.

​

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?

​

​​Maybe create a tree diagram:

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​

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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?

​

​​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?

​

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%

Fill in the Blanks

A basket contains five apples and seven peaches. You randomly select one piece of fruit and eat it. Then you randomly select another piece of fruit. What is the probability the first piece of fruit was an apple and the second piece was a peach?