Understanding Probability with an Unfair Die

The video tutorial explains the concept of an unfair die, where outcomes are not equally likely. It introduces the probability distribution of the die's face values and uses random variable notation to express events and probabilities. The tutorial demonstrates how to calculate various probabilities using a table and inequality symbols, providing examples for different scenarios. The video concludes with a summary of the key points discussed.

What is an unfair die?

• A die with more than six sides

• A die that is used in magic tricks

• A die with unequal probabilities for each face

• A die that is larger than a standard die

How is an event where the face value is exactly four expressed using random variable notation?

• X < 4

• X > 4

• X = 4

• X ≠ 4

What is the probability that the face value is exactly four?

• 0.16

• 0.14

• 0.11

• 0.03

What is the probability that the face value is one?

• 0.03

• 0.14

• 0.11

• 0.16

How do you calculate the probability that the face value is between four and six inclusive?

• Add probabilities of X=4, X=5, and X=6

• Subtract probabilities of X=4 and X=6

• Multiply probabilities of X=4, X=5, and X=6

• Divide probabilities of X=4 and X=6

What is the probability that the face value is less than three?

• 0.34

• 0.30

• 0.14

• 0.16

What is the probability that the face value is greater than or equal to five?

• 0.11

• 0.16

• 0.03

• 0.14

How do you express the probability that the face value is greater than one and less than or equal to three?

• X = 1 or X = 3

• X = 3 or X = 4

• X = 2 or X = 3

• X = 1 or X = 2

What is the probability that the face value is greater than one and less than or equal to three?

• 0.16

• 0.14

• 0.34

• 0.56

What is the sum of probabilities for the outcomes where X equals four, five, or six?

• 0.30

• 0.34

• 0.16

• 0.14