Gr 11 Math Ch 10 SUM: Probability

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Questions and Answers

What is the formula for the probability of two independent events A and B?

  • P(A) × P(B) (correct)
  • P(A) + P(B)
  • P(A) - P(B)
  • P(A) / P(B)

What is the definition of mutually exclusive events?

  • Two events that are independent of each other
  • Two events that cannot occur at the same time (correct)
  • Two events that have the same probability
  • Two events where the occurrence of one affects the probability of the other

What is the formula for the conditional probability of event A given event B?

  • P(A) × P(B)
  • P(A) + P(B)
  • P(A ∩ B) / P(B) (correct)
  • P(A) / P(B)

What is the formula for the probability of two dependent events A and B?

<p>P(A) × P(B | A) (A)</p> Signup and view all the answers

What is the notation for the union of two events A and B?

<p>A ∪ B (A)</p> Signup and view all the answers

What is the formula for the probability of the complement of event A?

<p>1 - P(A) (B)</p> Signup and view all the answers

What is the definition of dependent events?

<p>Two events where the occurrence of one affects the probability of the other (D)</p> Signup and view all the answers

What is the formula for the probability of the intersection of two independent events A and B?

<p>P(A) × P(B) (D)</p> Signup and view all the answers

What does the union of two events A and B represent?

<p>Outcomes in either event A or B or both (B)</p> Signup and view all the answers

What is the formula for the probability of three events A, B, and C using the general addition rule?

<p>P(A ∪ B ∪ C) = P(A) + P(B) + P(C) - P(A ∩ B) - P(A ∩ C) - P(B ∩ C) + P(A ∩ B ∩ C) (C)</p> Signup and view all the answers

What is the definition of mutually exclusive events?

<p>Events that cannot occur simultaneously (C)</p> Signup and view all the answers

What is the purpose of a tree diagram?

<p>To organize and visualize the possible outcomes of a sequence of events (C)</p> Signup and view all the answers

What is the formula for the probability of a path in a tree diagram?

<p>P(Path) = P(Event 1) × P(Event 2) × ... (D)</p> Signup and view all the answers

What is the purpose of a two-way contingency table?

<p>To test for independence between two events (D)</p> Signup and view all the answers

What is the formula for the probability of an event A given event B?

<p>P(A|B) = P(A and B) / P(B) (B)</p> Signup and view all the answers

What is the condition for independence between two events A and B?

<p>P(A and B) = P(A) × P(B) (D)</p> Signup and view all the answers

What does the intersection of three events A, B, and C represent?

<p>Outcomes in all three events A, B, and C (C)</p> Signup and view all the answers

What is the formula for the probability of two independent events A and B?

<p>P(A and B) = P(A) × P(B) (A)</p> Signup and view all the answers

What is the probability of event A occurring given that event B has occurred, if P(A and B) = 0.2 and P(B) = 0.5?

<p>0.25 (D)</p> Signup and view all the answers

If two events A and B are mutually exclusive, what is the value of P(A and B)?

<p>0 (D)</p> Signup and view all the answers

What is the probability of event A or event B occurring, if P(A) = 0.3, P(B) = 0.2, and P(A and B) = 0.1?

<p>0.4 (B)</p> Signup and view all the answers

If P(A) = 0.4 and P(B) = 0.5, what is the maximum possible value of P(A and B)?

<p>0.2 (A)</p> Signup and view all the answers

What is represented by the region outside the circle representing event A in a Venn diagram?

<p>The complement of event A (B)</p> Signup and view all the answers

If event A and event B are independent, what is the value of P(A and B) if P(A) = 0.2 and P(B) = 0.3?

<p>0.06 (D)</p> Signup and view all the answers

What is the probability of event A, if P(A') = 0.7?

<p>0.3 (B)</p> Signup and view all the answers

If P(A) = 0.2, P(B) = 0.3, and P(A or B) = 0.4, what is the value of P(A and B)?

<p>0.1 (A)</p> Signup and view all the answers

What is the correct formula for the probability of the union of three events A, B, and C?

<p>$P(A) + P(B) + P(C) - P(A \cap B) - P(A \cap C) - P(B \cap C) + P(A \cap B \cap C)$ (C)</p> Signup and view all the answers

What is the purpose of a contingency table?

<p>To test for independence between two events (B)</p> Signup and view all the answers

What does a branch in a tree diagram represent?

<p>A possible outcome of an event (C)</p> Signup and view all the answers

What is the correct formula for the conditional probability of event A given event B?

<p>$P(A \cap B) / P(B)$ (C)</p> Signup and view all the answers

What is the condition for independence between two events A and B?

<p>$P(A \cap B) = P(A) * P(B)$ (A)</p> Signup and view all the answers

What is the correct formula for the probability of a specific path in a tree diagram?

<p>$P(Event1) * P(Event2) * ...$ (D)</p> Signup and view all the answers

What is the purpose of the general addition rule in probability?

<p>To calculate the probability of the union of three events (A)</p> Signup and view all the answers

What does the intersection of three events A, B, and C represent?

<p>Outcomes in all three events A, B, and C (B)</p> Signup and view all the answers

What is the correct formula for the probability of an event A using a contingency table?

<p>$n(A) / n(Total)$ (C)</p> Signup and view all the answers

What is the purpose of tree diagrams?

<p>To visualize the outcomes of a sequence of events (D)</p> Signup and view all the answers

What is the probability of events A and B occurring if they are independent and P(A) = 0.4 and P(B) = 0.6?

<p>0.24 (A)</p> Signup and view all the answers

What is represented by the intersection of events A and B in a Venn diagram?

<p>Outcomes that are common to both events A and B (D)</p> Signup and view all the answers

What is the probability of event A or event B occurring if P(A) = 0.3, P(B) = 0.2, and P(A and B) = 0.1?

<p>0.4 (C)</p> Signup and view all the answers

What is the purpose of the conditional probability formula?

<p>To find the probability of event A occurring given that event B has occurred (A)</p> Signup and view all the answers

What is the probability of event A if P(A') = 0.8?

<p>0.2 (A)</p> Signup and view all the answers

What is the formula for the probability of the union of two mutually exclusive events A and B?

<p>P(A) + P(B) (A)</p> Signup and view all the answers

What is the probability of event A and event B occurring if P(A) = 0.3, P(B) = 0.4, and P(A and B) = 0.2?

<p>0.2 (C)</p> Signup and view all the answers

What is the purpose of the addition rule for non-mutually exclusive events?

<p>To find the probability of the union of two non-mutually exclusive events (B)</p> Signup and view all the answers

What is the probability of event A given event B, if the probability of event B is 0.4 and the probability of events A and B is 0.2?

<p>0.25 (C)</p> Signup and view all the answers

What is the purpose of using a tree diagram in probability?

<p>To visualize the possible outcomes of a sequence of events (C)</p> Signup and view all the answers

What is the formula for the probability of three events A, B, and C using the general addition rule?

<p>P(A) + P(B) + P(C) - P(A ∩ B) - P(A ∩ C) - P(B ∩ C) + P(A ∩ B ∩ C) (C)</p> Signup and view all the answers

What does the intersection of two events A and B represent?

<p>The outcomes that are in both event A and event B (C)</p> Signup and view all the answers

What is the condition for independence between two events A and B?

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

What is the purpose of a contingency table in probability?

<p>To test for independence between two events (B)</p> Signup and view all the answers

What is the formula for the probability of a path in a tree diagram?

<p>P(First Event) × P(Second Event) × ... (C)</p> Signup and view all the answers

What is represented by the branches of a tree diagram?

<p>The possible outcomes of a sequence of events (C)</p> Signup and view all the answers

What is the formula for the probability of an event A using a contingency table?

<p>n(A) / n(Total) (B)</p> Signup and view all the answers

What is the purpose of the general addition rule in probability?

<p>To calculate the probability of three or more events (A)</p> Signup and view all the answers

If P(A) = 0.4, P(B) = 0.3, and P(A and B) = 0.2, what is the probability of A or B occurring?

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

If event A is independent of event B, and P(A) = 0.3 and P(B) = 0.2, what is the probability of A and B occurring?

<p>0.06 (C)</p> Signup and view all the answers

What is the probability of event A given event B, if P(A and B) = 0.2 and P(B) = 0.5?

<p>0.4 (A)</p> Signup and view all the answers

If two events A and B are mutually exclusive, what is the value of P(A and B)?

<p>0 (A)</p> Signup and view all the answers

What is the probability of the complement of event A, if P(A) = 0.7?

<p>0.3 (D)</p> Signup and view all the answers

If P(A) = 0.5 and P(B) = 0.4, what is the maximum possible value of P(A and B)?

<p>0.2 (C)</p> Signup and view all the answers

What is represented by the region outside the circle representing event A in a Venn diagram?

<p>The complement of event A (C)</p> Signup and view all the answers

If event A and event B are independent, what is the value of P(A | B) if P(A) = 0.4 and P(B) = 0.3?

<p>0.4 (D)</p> Signup and view all the answers

What is the probability of the union of three events A, B, and C if P(A) = 0.3, P(B) = 0.2, P(C) = 0.1, P(A ∩ B) = 0.1, P(A ∩ C) = 0.05, P(B ∩ C) = 0.04, and P(A ∩ B ∩ C) = 0.01?

<p>0.35 (A)</p> Signup and view all the answers

A tree diagram is used to represent the outcomes of a sequence of two events. If the probability of event A is 0.3 and the probability of event B given event A is 0.4, what is the probability of the path A then B?

<p>0.12 (B)</p> Signup and view all the answers

In a contingency table, the count of event A and event B is 20, the count of event A is 30, and the total count is 100. What is the probability of event A given event B?

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

Events A and B are independent, and P(A) = 0.2, P(B) = 0.5. What is the probability of event A or event B occurring?

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

In a two-way contingency table, the count of event A is 30, the count of event B is 20, and the total count is 100. What is the probability of event A?

<p>0.3 (C)</p> Signup and view all the answers

Events A and B are mutually exclusive, and P(A) = 0.3, P(B) = 0.2. What is the probability of event A or event B occurring?

<p>0.4 (B)</p> Signup and view all the answers

A tree diagram is used to represent the outcomes of a sequence of two events. If the probability of event A is 0.4 and the probability of event B is 0.3, what is the probability of the path A then not B?

<p>0.28 (B)</p> Signup and view all the answers

In a contingency table, the count of event A is 20, the count of event B is 30, and the count of event A and B is 10. What is the probability of event A and event B occurring?

<p>0.1 (D)</p> Signup and view all the answers

Events A and B are independent, and P(A) = 0.4, P(B) = 0.6. What is the probability of event A and event B occurring?

<p>0.24 (C)</p> Signup and view all the answers

In a two-way contingency table, the count of event A and event B is 15, the count of event A is 30, and the count of event B is 25. What is the probability of event A given event B?

<p>0.6 (D)</p> Signup and view all the answers

What is the probability of event A given event B, if the probability of event B is 0.4, the probability of events A and B is 0.2, and events A and B are dependent?

<p>0.25 (A)</p> Signup and view all the answers

If events A and B are independent, and P(A) = 0.3, P(B) = 0.5, what is the probability of events A and B occurring?

<p>0.15 (A)</p> Signup and view all the answers

What is the probability of event A or event B occurring if P(A) = 0.2, P(B) = 0.3, and P(A and B) = 0.1?

<p>0.5 (D)</p> Signup and view all the answers

If events A and B are mutually exclusive, what is the value of P(A and B)?

<p>0 (A)</p> Signup and view all the answers

What is the probability of event A occurring if P(A') = 0.6?

<p>0.4 (B)</p> Signup and view all the answers

If P(A) = 0.4, P(B) = 0.5, and P(A or B) = 0.6, what is the value of P(A and B)?

<p>0.1 (C)</p> Signup and view all the answers

What is the probability of events A and B occurring if P(A) = 0.2, P(B) = 0.3, and they are independent?

<p>0.06 (C)</p> Signup and view all the answers

What is the probability of event A or event B occurring if P(A) = 0.4, P(B) = 0.5, and they are mutually exclusive?

<p>0.8 (B)</p> Signup and view all the answers

In a tree diagram, what is the correct way to calculate the probability of a specific sequence of events?

<p>Multiply the probabilities of each branch along the path (C)</p> Signup and view all the answers

What is the correct formula for the probability of three events A, B, and C using the general addition rule?

<p>P(A) + P(B) + P(C) - P(A ∩ B) - P(A ∩ C) - P(B ∩ C) + P(A ∩ B ∩ C) (A)</p> Signup and view all the answers

What is the purpose of a contingency table in probability?

<p>To compute probabilities and test for independence between events (C)</p> Signup and view all the answers

What is the correct formula for the probability of an event A given event B, using a contingency table?

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

What is represented by the intersection of two events A and B in a Venn diagram?

<p>The outcomes that are in both event A and event B (B)</p> Signup and view all the answers

What is the condition for independence between two events A and B?

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

What is the correct formula for the probability of two dependent events A and B?

<p>P(A) × P(B|A) (A)</p> Signup and view all the answers

What is the purpose of the general addition rule in probability?

<p>To calculate the probability of three events using the general addition rule (D)</p> Signup and view all the answers

What is the correct formula for the probability of the union of two events A and B?

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

What is the purpose of using a tree diagram in probability?

<p>To organize the outcomes of a sequence of events (C)</p> Signup and view all the answers

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