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The probability of event X occurring is the same as the prob
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30 Nov 2019, 00:04
30 Nov 2019, 00:04
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61% (00:53) correct
38% (00:46) wrong based on 130 sessions
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The probability of event X occurring is the same as the probability of event Y occurring. The events occur independently of each other.
A. Quantity A is Greater.
B. Quantity B is Greater.
C. Both are equal.
D. Cannot be determined from the given information.
Quantity A |
Quantity B |
The probability that both events occur |
The probability that neither event occurs. |
A. Quantity A is Greater.
B. Quantity B is Greater.
C. Both are equal.
D. Cannot be determined from the given information.
Re: The probability of event X occurring is the same as the prob
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14 Dec 2019, 02:51
14 Dec 2019, 02:51
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In these types of questions, one of the best ways is to substitute some of the values and try to make A as greater with one set of values and try to make B as greater with another set of values.
Lets Assume P(X) = P(Y) = 1
A --> (P(X)) (P(Y) ) = 1
B --> 0X0 = 0
A> B
Now assume
P(X) = P(Y) = 0.2
Then
A --> (P(X)) (P(Y) ) = (0.2)(0.2) = 0.04
B --> (0.8)(0.8) = 0.64
A<B
No definite answer. Hence, D is the right option.
Lets Assume P(X) = P(Y) = 1
A --> (P(X)) (P(Y) ) = 1
B --> 0X0 = 0
A> B
Now assume
P(X) = P(Y) = 0.2
Then
A --> (P(X)) (P(Y) ) = (0.2)(0.2) = 0.04
B --> (0.8)(0.8) = 0.64
A<B
No definite answer. Hence, D is the right option.
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Re: The probability of event X occurring is the same as the prob
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23 Sep 2021, 09:28
23 Sep 2021, 09:28
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huda wrote:
The probability of event X occurring is the same as the probability of event Y occurring. The events occur independently of each other.
A. Quantity A is Greater.
B. Quantity B is Greater.
C. Both are equal.
D. Cannot be determined from the given information.
Quantity A |
Quantity B |
The probability that both events occur |
The probability that neither event occurs. |
A. Quantity A is Greater.
B. Quantity B is Greater.
C. Both are equal.
D. Cannot be determined from the given information.
Given: The probability of event X occurring is the same as the probability of event Y occurring. The events occur independently of each other.
Let P(event X occurs) = p
This means we can also say that P(event Y occurs) = p
Useful property: P(Event A happening) = 1 - P(Event A not happening)
So, P(event X does not occur) = 1 - p
And P(event Y does not occur) = 1 - p
If events A and B are independent where P(A) = a and P(B) = b, then the probability that both events happen = ab
So, P(events X and B both occur) = (p)(p) = p²
Similarly, P(events X and B both do NOT occur) = (1 - p)(1 - p) = (1 - p)² = 1 - 2p + p²
So we have:
QUANTITY A: p²
QUANTITY B: 1 - 2p + p²
Subtract p² from both quantities to get:
QUANTITY A: 0
QUANTITY B: 1 - 2p
Add 2p to both quantities to get:
QUANTITY A: 2p
QUANTITY B: 1
Divide both quantities by 2 to get:
QUANTITY A: p
QUANTITY B: 0.5
Since the value of p can be less than 0.5, equal to 0.5, or greater than 0.5, the correct answer is D
