Gr 10 Math Ch 11: Probability Identities

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Questions and Answers

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?

<p>Double-counting the area where they intersect (C)</p> 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)?

<p>0.7 (C)</p> Signup and view all the answers

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

<p>Events A and B are mutually exclusive (B)</p> Signup and view all the answers

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

<p>Double counting of the intersecting area (B)</p> 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>P(A ∪ B) = P(A) + P(B) (C)</p> Signup and view all the answers

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

<p>The probability of the union is less than or equal to the sum of probabilities. (A)</p> Signup and view all the answers

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

<p>Venn diagrams (A)</p> 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>P(A ∩ B) (A)</p> Signup and view all the answers

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

<p>P(S) = 1 (D)</p> 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>P(A) + P(B) - P(A ,\cap B) (A)</p> 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>P(A ∪ B) will decrease as the overlap is considered. (D)</p> Signup and view all the answers

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

<p>The double counting of the intersection area in Venn diagrams. (B)</p> Signup and view all the answers

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

<p>The probability of the sample space consisting of all outcomes is certain. (A)</p> Signup and view all the answers

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

<p>It represents the individual probabilities without considering overlaps. (B)</p> Signup and view all the answers

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

<p>The intersection directly impacts the total probabilities of the union. (A)</p> Signup and view all the answers

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