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The Question & Answer (Q&A) Knowledge Managenet

The Internet has many places to ask questions about anything imaginable and find past answers on almost everything.

Table of Contents

- What is the formula for dependent probability?
- How do you find the probability of three independent events?
- How do you find the probability of multiple independent events?
- How do you find the probability of A and B if they are dependent?
- What is the probability that A or B occurs?
- How do you know if an event is dependent?
- Are A and B independent example?
- Is the following statement true or false if A and B are independent then A and B are independent?
- Is A and B are independent events then?
- What is the difference between disjoint and independent?
- Can two independent events occur at the same time?
- What does independent mean in probability?
- Under what conditions is an event a independent of itself?
- Are the events female and 0 activities independent?
- Are the events male and 5 plus activities independent?
- Are the events male and driver independent?
- Are the events homeowner and high school graduate independent?
- What is the probability that a randomly selected driver?
- What is the probability that a high risk borrower will default?
- Are the events female and driver independent?
- What is the probability that a randomly selected mortgage will not default?

If A and B are dependent events, then the probability of A happening AND the probability of B happening, given A, is P(A) × P(B after A).

The concept of independence applies to any number of events. For example, three events A,B,andC are independent if P(A∩B∩C)=P(A)⋅P(B)⋅P(C).

Probability of Two Events Occurring Together: Independent Just multiply the probability of the first event by the second. For example, if the probability of event A is 2/9 and the probability of event B is 3/9 then the probability of both events happening at the same time is (2/9)*(3/9) = 6/81 = 2/27.

The probability of A and B means that we want to know the probability of two events happening at the same time. There’s a couple of different formulas, depending on if you have dependent events or independent events. Formula for the probability of A and B (independent events): p(A and B) = p(A) * p(B).

The probability that Events A or B occur is the probability of the union of A and B. The probability of the union of Events A and B is denoted by P(A ∪ B) . If the occurrence of Event A changes the probability of Event B, then Events A and B are dependent.

Independent Events

- Two events A and B are said to be independent if the fact that one event has occurred does not affect the probability that the other event will occur.
- If whether or not one event occurs does affect the probability that the other event will occur, then the two events are said to be dependent.

Two events A and B are independent if the knowledge that one occurred does not affect the chance the other occurs. For example, the outcomes of two roles of a fair die are independent events. The outcome of the first roll does not change the probability for the outcome of the second roll.

Hence the events are independent but not mutually exclusive. Hence option [a] is incorrect. Hence the events A and B’ are independent, Since A and B’ are independent, we have A’ and B’ are also independent.

If A and B are independent events, then the events A and B’ are also independent. Proof: The events A and B are independent, so, P(A ∩ B) = P(A) P(B). From the Venn diagram, we see that the events A ∩ B and A ∩ B’ are mutually exclusive and together they form the event A.

Events are considered disjoint if they never occur at the same time; these are also known as mutually exclusive events. Events are considered independent if they are unrelated.

However, they are two distinct concepts. Mutually exclusive events are events that cannot occur simultaneously. The concept of independent events is not related to the simultaneous occurrence of the events, but it is only concerned with the influence of the occurrence of one event on another.

In probability, we say two events are independent if knowing one event occurred doesn’t change the probability of the other event.

Two events are independent, statistically independent, or stochastically independent if the occurrence of one does not affect the probability of occurrence of the other (equivalently, does not affect the odds).

Activities 0 1 2 − 3 4 − 5 + Total Male 22 83 58 37 200 Female 22 53 56 69 200 Total 44 136 114 106 400 (a) ” ” Are the events ” and activities” independent? female 0 because are Yes, P(female) and P(female|0 activities) equal. female − because is No, P(female and 1 − 2 activities) not zero.

(a) Are the events “male” and “5+ activities” independent? (a) No, because Upper P left parenthesis male right parenthesis and Upper P left parenthesis male| 5 plus activities right parenthesisP(male) and P(male|5+ activities) are not equal.

Answer: The probability of selecting a male is 0.3151. The events “male” and “driver” are not independent.

Are the events “homeowner” and “high school graduate” independent? Justify you answer. Because these two probabilities are not equal, the events “homeowner” and “high school graduate” are not independent.

The probability that a randomly selected driver fatality who was male was 35 to 54 years old is approximately 0,202 – Plastosy | M) = 11733%8865 – 030189~0.302 (Round to three decimal places as needed.)

A bank classifies borrowers as “high risk” or “low risk,” and 16% of its loans are made to those in the “high risk” category. Of all the bank’s loans, 5% are in default. It is also known that 40% of the loans in defaultare to high-risk borrowers.

Are the events”female”and”driver”independent? A. No. The occurrence of the event”female”does not affect the probability of the event “driver.”

47.22% probability that nine randomly selected mortgages will not default.