Probability Tree Model Quiz

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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) = length(A) / length(Omega)

P(A) = #(Omega) / #(A)

P(A) = area(A) / area(Omega)

P(A) = #(A) / #(Omega) (correct)

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?

$\frac{b - a}{d} \times P([a, d-c b])$

$\frac{b}{d-a} \times P([a, d-c b])$ (correct)

$\frac{b}{d} \times P([a, d-c b])$

$\frac{b}{d-c} \times P([a, d-c b])$

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 (correct)

By dividing the area of the square by the area of the event

By dividing the length of the event by the length of the square

By dividing the length of the square by the length of the event

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?

$\frac{b - a}{b} \times P([a, d-c b])$ Signup and view all the answers

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 Signup and view all the answers

What is the probability of getting one head and one tail when flipping two coins according to the provided information?

.5 Signup and view all the answers

In the context of the continuous model discussed, what does P(X = x) = 0 represent?

Probability of X being equal to x Signup and view all the answers

If P(X = x) = 0.[a, b] ⊂ [0, 1], what is the probability of X being in the interval [a, b]?

(b - a) Signup and view all the answers

In a discrete probability scenario, what does P(A) = #(Ω) / #(A) represent?

Probability of event A occurring Signup and view all the answers

What is the formula for calculating the probability of an event in a continuous model?

(d - c) / (b - a) Signup and view all the answers

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] Signup and view all the answers

What is the range of the probability function P(A) according to the provided text?

[0, 1] Signup and view all the answers

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 Signup and view all the answers

Which of the following formulas represents the normalization axiom of probability functions?

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

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) Signup and view all the answers

In probability theory, what does the symbol Ω represent?

The sample space Signup and view all the answers

If two events A and B are independent, which of the following statements is true?

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

Probability Tree Model Quiz

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