Gr 10 Math Ch 11: Probability Identities

What is the probability of observing an outcome from the sample space?

Undefined

0

1 (correct)

0.5

Which formula correctly calculates the probability of the union of two events A and B?

P(A union B) = P(A) + P(B) - P(A cap B) (correct)

P(A cap B) + P(A) + P(B)

P(A) + P(B)

P(A) - P(B) + P(A cap B)

What does the area of intersection in a Venn diagram represent?

The probability of both events A and B occurring at the same time (correct)

The total probability of event A

The probability of either event A or event B occurring

The total probability of event B

What is the result of adding the probabilities of two events without considering their intersection?

Double-counting the area where they intersect Signup and view all the answers

If P(A) = 0.3, P(B) = 0.5, and P(A ∩ B) = 0.1, what is P(A ∪ B)?

0.7 Signup and view all the answers

What happens if P(A ∩ B) is equal to zero?

Events A and B are mutually exclusive Signup and view all the answers

What does the probability identity for the union of two events help to correct?

Double counting of the intersecting area Signup and view all the answers

If two events A and B have no overlap, what is the identity used to calculate P(A ∪ B)?

P(A ∪ B) = P(A) + P(B) Signup and view all the answers

Which of the following statements best describes the relationship between probabilities of individual events and their union?

The probability of the union is less than or equal to the sum of probabilities. Signup and view all the answers

What geometric representation can be used to better understand the probability identity for the union of events?

Venn diagrams Signup and view all the answers

In the formula P(A ∪ B) = P(A) + P(B) - P(A ∩ B), which term accounts for the overlap between events?

P(A ∩ B) Signup and view all the answers

What is the mathematical notation for the sample space's probability?

P(S) = 1 Signup and view all the answers

What is the total probability represented when correctly applying the union identity for two events A and B?

P(A) + P(B) - P(A ,\cap B) Signup and view all the answers

If the probability of event A is 0.4 and event B is 0.6, what happens to the calculation of P(A ∪ B) if P(A ∩ B) is significantly high?

P(A ∪ B) will decrease as the overlap is considered. Signup and view all the answers

Which aspect is corrected by subtracting P(A ∩ B) in the union probability identity?

The double counting of the intersection area in Venn diagrams. Signup and view all the answers

What does the equation P(S) = 1 imply about the sample space in probability theory?

The probability of the sample space consisting of all outcomes is certain. Signup and view all the answers

When visualizing probabilities using Venn diagrams, what does the area representing P(A) + P(B) indicate before correction?

It represents the individual probabilities without considering overlaps. Signup and view all the answers

Which statement accurately describes the relationship between probabilities in the provided equations?

The intersection directly impacts the total probabilities of the union. Signup and view all the answers