Probability Quiz

The probability of hitting a circle in a dart-throwing scenario is given by the ratio of the area of the circle to the area of the wall. If the wall has an area of 100 square units and the circle has an area of 25 square units, what is the probability of hitting the circle?

• 0.1

• 0.25

• 0.5

• 1.0

In the context of dart throwing, what does 'event A' represent when calculating the probability P(A)?

• The dart hitting the wall.

• The dart hitting a specific blob B.

• The dart hitting the specified circle.

• The dart missing the wall.

Conditional probability tells us the chance that one thing will happen, given that another thing has already happened. Which of the following best describes P(A|B)?

• The probability of A given B has occurred.

• The probability of A and B both occurring.

• The probability of B given A has occurred.

• The probability of A or B occurring.

If blob A completely encloses blob B on the wall, what is the conditional probability P(A|B)?

• 0

• 0.5

• 1

• Cannot be determined.

If there is no overlap between blob A and blob B on the wall, what is the conditional probability P(A|B)?

• 0

• 0.5

• 1

• Cannot be determined.

How is the conditional probability P(B|A) calculated using areas?

• Area of A divided by Area of B.

• Area of B divided by Area of A.

• Area of A overlapping B divided by Area of B.

• Area of A overlapping B divided by Area of A.

What is the definition of the joint probability P(A,B)?

• The probability that A will occur given B has occurred.

• The probability that only A will occur.

• The probability that both A and B will occur.

• The probability that A or B will occur.

How can the joint probability P(A,B) be found using areas?

• Area of A divided by the area of the entire wall.

• Area of B divided by the area of the entire wall.

• Area of the overlap of regions A and B divided by the area of the entire wall.

• Area of the entire wall divided by the area of A overlapping B.

Another way to think about the joint probability P(A,B) is the probability that our dart will land in both A and B. Which formula describes this relationship using conditional probabilities?

• P(A,B) = P(A|B) * P(A)

• P(A,B) = P(A) + P(B)

• P(A,B) = P(A|B) * P(B)

• P(A,B) = P(A) / P(B)

The document mentions 'Finding marginal probabilities for 150 recent visitors at an ice cream shop'. What does 'marginal probability' generally refer to in a broader context like a confusion matrix?

• The probability of a single event occurring, without considering any other events.

• The probability of two events occurring together.

• The probability of an event occurring given another event.

• The probability of misclassification.