Understanding Probability in Candy Vending Machines

The video tutorial explains how Lisa manages a 'Random Candy' vending machine, focusing on setting and solving a probability inequality. Lisa wants to adjust the probability of getting 'Honey Bunny' candy to ensure that the chance of getting a different candy twice in a row is more than 2.25 times the probability of getting 'Honey Bunny' once. The tutorial guides through setting up the inequality, solving it using algebraic methods, and concludes that the probability of getting 'Honey Bunny' must be less than 0.25.

What is the main issue Lisa is facing with her 'Random Candy' vending machine?

• She needs to fix a mechanical issue.

• She wants to change the machine's location.

• She needs to adjust the probability of getting 'Honey Bunny'.

• She wants to increase the number of candies.

How is the probability of getting a candy other than 'Honey Bunny' represented?

• 1 - p

• 1 + p

• p - 1

• p

What is the inequality that needs to be solved in this problem?

• p > 2.25

• p^2 - 1 > 2.25p

• 1 - p^2 > 2.25p

• 1 - p > 2.25p

What is the first step in solving the inequality 1 - p^2 > 2.25p?

• Divide both sides by p.

• Multiply both sides by 2.

• Subtract 2.25p from both sides.

• Add 2.25p to both sides.

What is the simplified form of the inequality after expanding 1 - p^2?

• 1 + p^2 > 2.25p

• p^2 + 2p + 1 > 2.25p

• 1 - 2p + p^2 > 2.25p

• p^2 - 2p + 1 > 2.25p

What are the roots of the quadratic equation derived from the inequality?

• 1/5 and 6

• 1/2 and 3

• 1/3 and 5

• 1/4 and 4

What condition must be true for the product of two terms to be greater than zero?

• One term must be zero.

• Both terms must be zero.

• One term must be positive and the other negative.

• Both terms must be positive or both must be negative.

What is the final constraint on the probability of getting 'Honey Bunny'?

• p must be greater than 1

• p must be less than 0

• p must be greater than 4

• p must be less than 1/4

Why can't the probability of getting 'Honey Bunny' be greater than 4?

• Because it would make the machine malfunction.

• Because probabilities must be between 0 and 1.

• Because it would be too expensive.

• Because it would violate candy regulations.

What is the final inequality that models the problem?

• 1 - p^2 < 2.25p

• p^2 + 1 < 2.25p

• 1 - p^2 > 2.25p

• p^2 - 1 > 2.25p