Understanding Conditional Probabilities and the Alternate Addition Rule

The video tutorial explains the probability of having cake or pie at holiday meals using the addition rule. It introduces the traditional and conditional probability formulas and derives an alternate addition rule using conditional probabilities. A proof is provided to show the equivalence of the probability of intersection and the product of probabilities. Two examples are given: one for calculating the probability of having cake or pie, and another for voting probabilities in a prom scenario.

What is the main challenge in determining the probability of a family having cake or pie?

• Inaccurate percentage of families having pie

• Unknown probability of having both cake and pie

• Lack of data on cake consumption

• No information on holiday meals

Which formula is used to calculate the probability of A or B?

• Traditional addition rule

• Multiplication rule

• Bayes' theorem

• Conditional probability formula

How is the probability of the intersection of two events calculated using conditional probability?

• By adding the probabilities of each event

• By multiplying the probability of one event by the conditional probability of the other

• By subtracting the probability of one event from the other

• By dividing the probability of one event by the other

What does the proof using a two-way table demonstrate?

• The probability of A and B is equal to the product of A and B given A

• The probability of A or B is always greater than 1

• The probability of A and B is independent of A

• The probability of A and B is less than the probability of A

In the example of holiday meals, what is the probability of a family having cake or pie?

• 0.638

• 0.42

• 0.34

• 0.29

What is the probability that a student will vote for either Zack or Taylor?

• 0.7

• 0.54

• 0.904

• 0.48

Which rule is used when a conditional probability is given instead of the intersection probability?

• Traditional addition rule

• Alternate addition rule

• Bayes' theorem

• Multiplication rule