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Cloud moderators
13/12/2017 at 16:30
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Xera and Yeta use this method to decide who will sit in the front passenger seat of the car. Xera throws a standard six-sided die, after which Yeta picks a card from a standard deck of 52 cards, with replacement. They continue to take turns die-throwing and card-picking until either Xera wins by rolling a four or Yeta wins by picking a card with a four. What is the probability that Yeta wins? Express your answer as a common fraction.

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    Lê Quốc Trần Anh Coordinator 29/12/2017 at 17:57

    The probability that Xera has a four is: \(1:6=\dfrac{1}{6}\)

    The probability that Yeta has a four is: \(4:52=\dfrac{1}{13}\) (A standard deck has 4 cards of four)

    So the probability that Yeta wins is: \(\dfrac{1}{13}:\left(\dfrac{1}{6}+\dfrac{1}{13}\right)=\dfrac{6}{19}\)

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    FA Liên Quân Garena 30/12/2017 at 21:49

    The probability that Xera has a four is: 1:6=16

    The probability that Yeta has a four is: 4:52=113

     (A standard deck has 4 cards of four)

    So the probability that Yeta wins is: 113:(16+113)=619


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Cloud moderators
18/12/2017 at 08:51
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Given the expression  \(\dfrac{n^2-9}{n^2-4}\)  , for how many positive integers n from 1 to 2016, inclusive, is the GCF of the numerator and denominator greater than 1?


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Cloud moderators
18/12/2017 at 08:53
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The digital clock shown can display up to four digits to represent the hour and the minute. For how many minutes in a 12-hour period does the digit 0 appear on the clock? undefined


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Kaya Renger Coordinator
20/12/2017 at 20:35
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Given x,y are two positive real numbers (x,y differ to 0) satisfy \(5x^2+\dfrac{y^2}{4}+\dfrac{1}{4x^2}=\dfrac{5}{2}\)

Find minimum and maximum value of expression \(A=2013-xy\) 

Source : https://olm.vn/hoi-dap/question/1113825.html


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Nguyễn Hưng Phát
21/12/2017 at 16:33
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Given a triangle ABC,the point E on AB and the point F on AC such that EF//BC.Prove that:SCEF\(\le\dfrac{1}{4}\)SABC


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Nguyễn Hưng Phát
21/12/2017 at 16:36
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The three heights of a triangle are proportional to 3,4 and 5.Is the triangle an acute,right ,or obtuse triangle?


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Cloud moderators
21/12/2017 at 16:37
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A cube has one red, one green, one yellow and three blue faces. How many distinct cubes satisfying this description are possible? 


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Kaya Renger Coordinator
23/12/2017 at 14:42
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Find all integer value of x,y know : \(y^2=x\left(x+1\right)\left(x+2\right)\left(x+3\right)\)

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    FC Alan Walker 16/03/2018 at 13:31

    We have: \(y^2=x\left(x+1\right)\left(x+2\right)\left(x+3\right)\)

               \(\Leftrightarrow y^2+1=x\left(x+1\right)\left(x+2\right)\left(x+3\right)+1\)

               \(\Leftrightarrow y^2+1=\left(x^2+3x+1\right)^2\)

    \(\Rightarrow y=0\) (Because \(y^2\) and \(\left(x^2+3x+1\right)^2\) is two consecutive square numbers)

    \(\Rightarrow\left[{}\begin{matrix}x=0\\x+1=0\\x+2=0\\x+3=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=0\\x=-1\\x=-2\\x=-3\end{matrix}\right.\)

    So x=0; x=-1; x=-2; x=-3.


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Cloud moderators
21/12/2017 at 16:35
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Eight points on a circle are labeled. How many chords can be drawn connecting any two of these points? 


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Cloud moderators
21/12/2017 at 16:35
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Tad draws three cards at random, without replacement, from a deck of ten cards numbered 1 through 10. What is the probability that no two of the cards drawn have numbers that differ by 1? Express your answer as a common fraction.


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