17 Questions
In the context of probability, if an event A is defined as a subset of the sample space Omega and P(A) is the probability of event A, which of the following formulas correctly represents the probability of A in a discrete model?
P(A) = #(A) / #(Omega)
If [a, b] is a subset of [c, d], and P([a, d-c b]) is given, how can the probability P(X = x) be calculated in the continuous model?
$\frac{b}{d-a} \times P([a, d-c b])$
When treating a unit square like a dartboard for a probability experiment, how is the probability of a specific event calculated in the continuous model?
By dividing the area of the event by the area of the square
Given a unit interval [c,d] and interval [a,b] where [a,b] is a subset of [c,d], how can the probability P(A) be calculated in a discrete model?
$\frac{b - a}{b} \times P([a, d-c b])$
When calculating probabilities in a continuous model using a unit square, what does the ratio $\frac{area(A)}{area(\Omega)}$ represent?
The proportion of outcomes in A compared to all possible outcomes
What is the probability of getting one head and one tail when flipping two coins according to the provided information?
.5
In the context of the continuous model discussed, what does P(X = x) = 0 represent?
Probability of X being equal to x
If P(X = x) = 0.[a, b] ⊂ [0, 1], what is the probability of X being in the interval [a, b]?
(b - a)
In a discrete probability scenario, what does P(A) = #(Ω) / #(A) represent?
Probability of event A occurring
What is the formula for calculating the probability of an event in a continuous model?
(d - c) / (b - a)
If the interval [c, d] is given where P(X = x) = 0.[a, b] ⊂ [c, d], what does the expression d-c represent?
Length of the interval [c, d]
What is the range of the probability function P(A) according to the provided text?
[0, 1]
Which of the following statements is true about the additivity axiom of probability functions?
P(A ∪ B) = P(A) + P(B) if A, B are disjoint
Which of the following formulas represents the normalization axiom of probability functions?
P(Ω) = 1
What is the correct formula for the additivity axiom when events A and B are not disjoint?
P(A ∪ B) = P(A B) + P(B A) + P(A ∩ B)
In probability theory, what does the symbol Ω represent?
The sample space
If two events A and B are independent, which of the following statements is true?
P(A ∩ B) = P(A) × P(B)
Test your knowledge of probability using a tree model to calculate the likelihood of getting two tails, one head and one tail, or other combinations of coin flips. Understand the concept of tree diagrams in probability theory.
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