math q

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1

<p>Two white chips and two black chips are placed in a bag. Two chips are randomly drawn from the bag, replacing the chip in the bag after each draw. What is the probability that exactly one white chip will be drawn from the bag in these two draws??
a) 1/8
b) 1/4
c) 1/3
d) 1/2
e) 3/4</p>

<p>im pretty sure my method is correct, as is my answer, but the answer key i have gives something else. try it and tell me what you get and why please!!
thanks!!
i'll post my answer and the test's answer after some replies...</p>

2

<p>i got C,im not sure i understood the prob correctly,but heres how i see it.
there are 4 chips,u draw 2.
so u draw the first one,lets say black. 1/2 prob for chosoing blk
3 left,u wanna draw white, 2/3 prob
multiply both prob, = 1/3 C?</p>

3

<p>A. You are replacing the chip after each draw, thus total remains uchanged.</p>

<p>first draw
2/4</p>

<p>replace
second draw, there's 2 black chips as well
2/4
= 4/16 = 1/8</p>

4

<p>^Quix, 4/16 is equal to 1/4, but I think it's 1/4 B, which is probably what you meant.</p>

5

<p>OO oh thats y,u draw and pput it back right after, before the 2nd draw -.-</p>

6

<p>ANSWER IS DEFINITELY D.</p>

<p>Chance you get white first, black later = (1/2)<em>(1/2) = 1/4
Chance you get black first, white later = (1/2)</em>(1/2) = 1/4</p>

<p>Add them up, you get 1/4 + 1/4 = 1/2</p>

<p>The reason why Quix is wrong is that you have to account for the two permutations, of white first black later or white later black first.</p>

<p>Use a probability tree.</p>

<p>Throw no. Possible outcomes
First throw ..................White (50%)..........................................Black (50%).........
Second throw .........White (25%)....Black (25%)..................White (25%)....Black (25%)</p>

<p>Hence, you have 25% chance of white white, white black, black white, black black.</p>

<p>Adding up white black and black white, you get 50% or 1/2.</p>

7

<p>chance of getting white first time is 1/2(order doesn't matter), chance of getting black second time is also 1/2. so chance of getting one white and one black, is 1/2*1/2 =1/4</p>

8

<p>Please give us the answer.</p>

9

<p>Kevin2400, the thing is that you forgot that you can get black first time and white first time, which would also satisfy the condition of "exactly one white chip will be drawn from the bag in these two draws".</p>

<p>So you have 1/4 white first black second AND 1/4 black first white second.</p>

<p>Add them up to give 1/2.</p>

10

<p>the answer the test gives is D: 1/2
Fiona is right....</p>

11

<p>i am confused there's no way this can be a realistic sat math q right??</p>

<p>its from some test prep co. and its amazing how this problem, which tripped up so many people who are good at math (like me, 800 on the real thing) and its a question number 5 on the 20 q math section</p>

12

<p>^real 800 students get this. Is that 800 on QAS or the actual sitting of an SAT?</p>

13

<p>800 real SAT; 800 QASs; 800 MathII; 5 Calc BC; 80 PSAT
im not bad at math
and if i look up the posts correctly, you got it wrong shiomi....</p>

<p>the answer is D:1/2</p>

<p>i just dont remember the intricacies of probability</p>

14

<p>omg that was surprising lol. i dont think this will appear on the actual SAT. SAT tests the basic probability like the real basics...</p>

<p>dang...</p>

15

<p>Two white chips and two black chips are placed in a bag. Two chips are randomly drawn from the bag, replacing the chip in the bag after each draw. What is the probability that exactly one white chip will be drawn from the bag in these two draws??
a) 1/8
b) 1/4
c) 1/3
d) 1/2
e) 3/4</p>

<p>Answer) The case can be : White chip first, then black chip OR black chip first, then white chip.</p>

<p>So, prob. = (2/4)<em>(2/4) + (2/4)</em>(2/4)
= 2*(2/4)(2/4) = 1/2</p>

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16

<p>You guys are like over complicating things.
If you only need one white, then the other draw doesn't matter.
Chances of getting a white is 1/2. So that should be enough.</p>

17

<p>That's a very erroneous way of thinking about it, Timmy. It just happens that for this case, the end results are the same. </p>

<p>What if you have 30% white and 70% black? What's the chances of getting one white in two draws?</p>

<p>Hint: It isn't 30%.</p>

18

<p>Exactly. You're taking a very specific case</p>

19

<p>Ah, I see.
thanks for clearing things up</p>