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0<p<1
[#permalink]
26 Aug 2021, 01:52
26 Aug 2021, 01:52
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Question Stats:
3% (00:45) correct
96% (01:05) wrong based on 27 sessions
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\(0<p<1\)
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
Quantity A |
Quantity B |
The greatest value of \(p(1-p)\) |
\(\frac{1}{2}\) |
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
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0<p<1
[#permalink]
30 Aug 2021, 01:12
30 Aug 2021, 01:12
2
Carcass wrote:
pick a number for p that must be a fraction
Now if p=1/2 we do have 1/2*1/2 and the greatest value is still 1/2 and the answer is C
But if we have 1/4 we do have 1/4*3/4 and the greatest value is 3/4 which is > 1/2 and the answer is A
The answer should be D and not C as reported by the book.
I also wait confirm from others mod rx10 KarunMendiratta
Now if p=1/2 we do have 1/2*1/2 and the greatest value is still 1/2 and the answer is C
But if we have 1/4 we do have 1/4*3/4 and the greatest value is 3/4 which is > 1/2 and the answer is A
The answer should be D and not C as reported by the book.
I also wait confirm from others mod rx10 KarunMendiratta
Carcass
The highlighted part would be 1/2*1/2 = 1/4 and 1/4*3/4 = 3/16
The answer must be Col. B
Let us solve this question using Quadratic function (Parabola);
\(f(p) = p(1-p)\)
\(f(p) = -p^2 + p\)
In a Quadratic function with a < 0, the maximum value is y-coordinate of the vertex
x-coordinate of the vertex \(= \frac{-b}{2a} = \frac{-1}{2(-1)} = \frac{1}{2}\)
y-coordinate of the vertex \(= -(\frac{1}{2})^2 + \frac{1}{2} = 1/4\)
Col. A: \(\frac{1}{4}\)
Col. B: \(\frac{1}{2}\)
Hence, option B
Attachments
p(1-p) vs 0.5.png [ 21.6 KiB | Viewed 2866 times ]
General Discussion
Re: 0<p<1
[#permalink]
29 Aug 2021, 23:47
29 Aug 2021, 23:47
greatest value of p(1-p) will be 1/4
[and not 1/2 .. please note it has not asked the value of x at which p(1-p) will be greatest .. which is at x=1/2]
hence, answer should be B
Carcass , please provide your comments.
Thanks!
[and not 1/2 .. please note it has not asked the value of x at which p(1-p) will be greatest .. which is at x=1/2]
hence, answer should be B
Carcass , please provide your comments.
Thanks!
