Conditional Probability and Event Analysis

The video tutorial explains the probability of events E and F, their union, and intersection. It covers how to calculate the intersection probability using the union formula and explores conditional probabilities of E given F and F given E. The tutorial uses visual aids to help understand these concepts within probability spaces.

What is the probability of event E?

• 0.3

• 0.6

• 0.7

• 0.2

What is the probability of the union of events E and F?

• 0.7

• 0.2

• 0.6

• 0.3

Which formula is used to calculate the probability of the union of two events?

• P(E ∩ F)

• P(E) * P(F)

• P(E) + P(F) - P(E ∩ F)

• P(E) + P(F)

What is the calculated probability of the intersection of events E and F?

• 0.4

• 0.3

• 0.2

• 0.1

What is the probability of the non-intersection part of event E?

• 0.1

• 0.2

• 0.3

• 0.4

How is the conditional probability of E given F calculated?

• P(F) / P(E)

• P(E) / P(F)

• P(F ∩ E) / P(E)

• P(E ∩ F) / P(F)

What is the conditional probability of E given F?

• 1/2

• 1/3

• 1/4

• 2/3

How is the conditional probability of F given E calculated?

• P(E) / P(F)

• P(F ∩ E) / P(F)

• P(E ∩ F) / P(E)

• P(F) / P(E)

What is the conditional probability of F given E?

• 3/4

• 1/2

• 1/3

• 2/3

Why are conditional probabilities not equal when the order is switched?

• Because the denominator changes

• Because the intersection is always zero

• Because probabilities are always equal

• Because the numerator changes