Probability: Exhaustive, Mutually Exclusive, and Independent Events

The video tutorial covers key probability concepts, including exhaustive, mutually exclusive, and independent events. It explains each concept with definitions, examples, and relevant formulas. The tutorial also demonstrates how to calculate probabilities for these events using examples like card decks and dice rolls. Key formulas, such as the probability of A union B, are highlighted for understanding and application.

What does it mean for two events to be exhaustive?

• They are independent of each other.

• They have no elements in common.

• Their intersection is the universal set.

• Their union covers the entire universal set.

In the context of mutually exclusive events, what is true about their intersection?

• It is equal to the universal set.

• It is equal to the empty set.

• It is equal to the union of the events.

• It is equal to the probability of the events.

Which of the following is the correct formula for the probability of A union B?

• P(A) - P(B) + P(A ∩ B)

• P(A) + P(B) - P(A ∩ B)

• P(A) - P(B) - P(A ∩ B)

• P(A) + P(B) + P(A ∩ B)

In the example with a deck of cards, how many picture cards are there?

• 10

• 12

• 14

• 16

What does it mean for two events to be independent?

• The outcome of one affects the likelihood of the other.

• The outcome of one does not affect the likelihood of the other.

• They have no elements in common.

• Their union is the universal set.

Which symbol is used to denote 'given' in probability?

• |

• &

• ∩

• ∪

How can you test if two events are independent?

• Check if P(A ∩ B) = P(A) * P(B)

• Check if P(A ∩ B) = P(A) / P(B)

• Check if P(A ∩ B) = P(A) - P(B)

• Check if P(A ∩ B) = P(A) + P(B)

In the dice example, what is the probability of rolling a 6 with the first die?

• 1/5

• 1/6

• 1/4

• 1/3

What is the probability of A intersection C in the dice example?

• 1/24

• 1/72

• 1/36

• 1/12

Which formula is emphasized as important to remember in the recap?

• P(A ∩ B) = P(A) * P(B)

• P(A ∪ B) = P(A) + P(B) - P(A ∩ B)

• P(A ∪ B) = P(A) - P(B) + P(A ∩ B)

• P(A ∩ B) = P(A) + P(B)