Multinomial Probabilities and Marble Selection

The video tutorial explains multinomial probabilities using a marble selection problem. It covers the calculation of probabilities for different combinations of red, green, and black marbles selected with replacement. The tutorial distinguishes multinomial from binomial probabilities and provides step-by-step calculations for two examples, demonstrating how to use factorials and probability powers to find the desired outcomes.

How many red marbles are in the box?

• Six

• Ten

• Four

• Twenty

What is the probability of selecting a green marble?

• 3/10

• 1/5

• 1/4

• 1/2

Which of the following best describes multinomial probabilities?

• Only two possible outcomes

• Multiple independent trials with multiple outcomes

• Dependent trials with two outcomes

• Single trial with multiple outcomes

What is the factorial of 8 used for in the first example?

• Calculating the total number of marbles

• Determining the number of ways to select marbles

• Finding the probability of a single marble

• Converting probabilities to percentages

In the first example, what is the exponent used for the probability of selecting a red marble?

• 2

• 3

• 4

• 5

What is the probability of selecting a black marble in the first example?

• 3/10

• 1/5

• 1/2

• 1/12

In the second example, how many black marbles are selected?

• Two

• Four

• Five

• Three

What is the factorial of 3 used for in the second example?

• Converting probabilities to percentages

• Finding the probability of a single marble

• Determining the number of ways to select marbles

• Calculating the total number of marbles

What is the probability of selecting a red marble in the second example?

• 1/2

• 1/12

• 1/5

• 3/10

How is a decimal converted to a percentage?

• Add 100 and add a percent sign

• Multiply by 100 and add a percent sign

• Subtract 100 and add a percent sign

• Divide by 100 and add a percent sign