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Directions: Select one of the following answer choices.
Q. p is the probability that event E will occur, and s is the probability that event E will not occur.
Quantity A: p + s
Quantity B: ps
- a)Quantity A is greater.
- b)Quantity B is greater.
- c)The two quantities are equal.
- d)The relationship cannot be determined from the information given.
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
Directions: Select one of the following answer choices.Q. p is the pr...
Analysis:
To find the relationship between the quantities A and B, we need to understand what they represent and how they are related to each other.
Quantity A: p - s
This quantity represents the difference between the probability of event E occurring (p) and the probability of event E not occurring (s).
Quantity B: ps
This quantity represents the product of the probability of event E occurring (p) and the probability of event E not occurring (s).
Understanding the relationship:
To determine the relationship between A and B, let's evaluate them separately.
Evaluating Quantity A:
p - s
The probability of an event occurring (p) is always greater than the probability of the event not occurring (s) because the sum of all possible outcomes in a probability space is always 1. Therefore, p > s.
Evaluating Quantity B:
ps
The product of two probabilities (p and s) will always be less than or equal to the individual probabilities. This is because the product represents the probability of two independent events both occurring. If either event has a probability less than 1, then the product will be less than the individual probabilities. Therefore, ps ≤ p and ps ≤ s.
Conclusion:
From the above evaluations, we can conclude that Quantity A (p - s) is always greater than Quantity B (ps). Therefore, the correct answer is option A: Quantity A is greater.
Note:
It is important to note that without any specific values of p and s, we cannot determine the exact relationship between A and B. However, based on the general principles of probability, we can conclude that A will always be greater than B.
To find the relationship between the quantities A and B, we need to understand what they represent and how they are related to each other.
Quantity A: p - s
This quantity represents the difference between the probability of event E occurring (p) and the probability of event E not occurring (s).
Quantity B: ps
This quantity represents the product of the probability of event E occurring (p) and the probability of event E not occurring (s).
Understanding the relationship:
To determine the relationship between A and B, let's evaluate them separately.
Evaluating Quantity A:
p - s
The probability of an event occurring (p) is always greater than the probability of the event not occurring (s) because the sum of all possible outcomes in a probability space is always 1. Therefore, p > s.
Evaluating Quantity B:
ps
The product of two probabilities (p and s) will always be less than or equal to the individual probabilities. This is because the product represents the probability of two independent events both occurring. If either event has a probability less than 1, then the product will be less than the individual probabilities. Therefore, ps ≤ p and ps ≤ s.
Conclusion:
From the above evaluations, we can conclude that Quantity A (p - s) is always greater than Quantity B (ps). Therefore, the correct answer is option A: Quantity A is greater.
Note:
It is important to note that without any specific values of p and s, we cannot determine the exact relationship between A and B. However, based on the general principles of probability, we can conclude that A will always be greater than B.
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Community Answer
Directions: Select one of the following answer choices.Q. p is the pr...
Since event E will either occur or not occur, it follows that p + s = 1, and the value of Quantity A is always 1. Since Quantity B is the product of the two probabilities p and s, you need to look at its value for the cases p = 1, p = 0, and 0 < p="" />< 1="" .="" if="" p="1," then="" s="0;" similarly,="" if="" p="0," then="" s="1." in="" both="" cases,="" ps="" is="" equal="" to="" />
If 0 < p="" />< 1,="" both="" p="" and="" s="" are="" positive="" and="" less="" than="" 1,="" so="" ps="" is="" positive="" and="" less="" than="" 1.="" since="" quantity="" a="" is="" equal="" to="" 1="" and="" quantity="" b="" is="" less="" than="" 1,="" the="" correct="" answer="" is="" choice="" />
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Directions: Select one of the following answer choices.Q. p is the probability that event E will occur, and s is the probability that event E will not occur.Quantity A: p + sQuantity B: psa)Quantity A is greater.b)Quantity B is greater.c)The two quantities are equal.d)The relationship cannot be determined from the information given.Correct answer is option 'A'. Can you explain this answer?
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Directions: Select one of the following answer choices.Q. p is the probability that event E will occur, and s is the probability that event E will not occur.Quantity A: p + sQuantity B: psa)Quantity A is greater.b)Quantity B is greater.c)The two quantities are equal.d)The relationship cannot be determined from the information given.Correct answer is option 'A'. Can you explain this answer? for GRE 2024 is part of GRE preparation. The Question and answers have been prepared according to the GRE exam syllabus. Information about Directions: Select one of the following answer choices.Q. p is the probability that event E will occur, and s is the probability that event E will not occur.Quantity A: p + sQuantity B: psa)Quantity A is greater.b)Quantity B is greater.c)The two quantities are equal.d)The relationship cannot be determined from the information given.Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for GRE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Directions: Select one of the following answer choices.Q. p is the probability that event E will occur, and s is the probability that event E will not occur.Quantity A: p + sQuantity B: psa)Quantity A is greater.b)Quantity B is greater.c)The two quantities are equal.d)The relationship cannot be determined from the information given.Correct answer is option 'A'. Can you explain this answer?.
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