SAT II Math IIC question

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1

<p>Hi~~</p>

<p>So I was doing an online sparknotes practice test, and I came across this probability question that I got wrong:</p>

<p>A jar contains two black marbles and one white marble. If a marble is selected from the jar and removed and then a second marble is selected from the jar, what is the probability that the second marble selected is white?</p>

<p>(A) 1/6<br>
(B) 1/3<br>
(C) 1/2<br>
(D) 2/3<br>
(E) 5/6</p>

<p>I chose C since there's two ways of getting a white marble. If the first one chosen was a black marble, then the probability would be 1/2. If the first one was white, then the probability would be 0. I added those to get 1/2, but it says it's incorrect. I read the sparknotes explanation but am so confused now. Sparknotes says:</p>

<p>There are three marbles in the jar and each one has an equal probability of being the second one chosen. Only one of them is white, so the probability is 1/3. 1/2might look tempting, but it’s incorrect because there’s a chance that the white marble would be removed in the first draw.</p>

<p>Why would the probability be 1/3 if it were asking for the probability of selecting a white marble on the SECOND trial? help! haha</p>

<p>Thanks!</p>

2

<p>I totally understand why you are confused…I took this test Sparknotes #3 and I got it right. The fact that the they are refering to the second marble makes no differance. They are asking about the second marble when all 3 are present. As you said, it depends whether I choose the black or white one on the first try. Everyone agrees that the first try is a 1/3 chance, therefore, the second try must also be a 1/3 chance! Each one has an equal probability of being the second one chosen. If I say I have letters A, B, and C in a bag, what is the chance that the second one chosen is B? It is 1/3 of a chance because now I am looking at all 3…yes, once the first one happens what you said is true, but at this point “in the game” it is 1/3…dont over analyze!</p>

3

<p>1/3</p>

<p>try 1 has to be black so that’s 2/3, try 2 has to be white, so 1/2 (already pulled a black marble)</p>

<p>1/2*2/3=2/6 which simplifies down to 1/3</p>