<p>I did not understand the following problems, and I did not understand Chung's explanations. </p>
<p>1) A jar contains four white marbles and two blue marbles, all the same size. A marble is drawn at random and NOT replaced. A second marble is then drawn from the jar. What is the probability that one white and one blue marble are drawn?</p>
<p>a) 8/15 b) 4/15 c) 1/3 d) 1/2 e) 2/3</p>
<p>2) How many gallons of water must be added to 40 gallons of 10% alcohol solution to produce a 8% alcohol solution?</p>
<p>a) 5 b) 8 c) 10 d) 12 e) 20</p>
<p>3) How many quarts of alcohol must be added to 10 quarts of a 25% alcohol solution to produce 40% alcohol solution?</p>
<p>a) 2.5 quarts b) 8 quarts c) 10 quarts d) 15 quarts e) 20 quarts</p>
<p>I don't understand that whole ''% of a solution'' concept. I don't understand how to use the formula for % of a solution. Can someone explain these problems step by step? Or at least better than Chung? Thanks.</p>
<p>Dont worry, I think I can explain it to you. They may seem tricky but you just have to set up the equations right and read the question properly.</p>
<p>for the first one there are 6 marbles in total. They are asking you the chances of getting a blue and white marble on two tries. Well when you first pick a marble there are 4/6 white marbles. Then to pick a blue marble on second try there are 2/5. multiply them </p>
<p>4/6 *2/5 = 8/30 = 4/15</p>
<p>it doesnt matter which one you choose first. If you decided to put blue first then it would be 2/3 times 4/5 which equals 4/15. Simple right?</p>
<p>For the second one, you have to set up the equation properly and it becames a piece of cake. You have 40 gallons of a solution. In that solution 10% is alcohol or .1 *40 = 4.
you are trying to make it an 8% solution and you need to know how much water you need to add. so the alcohol value stays the same but the total gallon value changes.</p>
<p>4/40 + x = 8/100 (alcohol/gallons + what you are adding = 8% alcohol). Equation is set up just solve.</p>
<p>4 = 40(8) + x(8)/100</p>
<p>4 = 320 + 8x/100</p>
<p>400 = 320 + 8x</p>
<p>80 = 8x</p>
<p>x = 10 </p>
<p>There you have it. Just a matter of setting up the equation properly.</p>
<p>For the last one its the exact same process as above except your changing both the alcohol value and the total gallons. You have ten gallons and 1/4 of it is alcohol or 2.5 quarts is alcohol. Now you need to add some more quarts so that the entire alcohol solution becomes 40%. so</p>
<p>2.5 + x/10 +x = 40/100 (current alcohol %tage + additional alcohol/number of + additional alcohol = 40%)</p>
<p>now solve</p>
<p>2.5 + x = 40x + 400/100</p>
<p>250 + 100x = 40x + 400</p>
<p>-150 = -60x</p>
<p>x = 2.5 quarts</p>
<p>Again just read the problem and set up the equation properly. It will help you immensly later on if you follow this method.</p>
<p>^ Good explanations for the alcohol. But you did 1) wrong.</p>
<p>I believe the question isn’t asking what the possibility is of drawing a white, and THEN a blue marble, but just having 1 blue and 1 white in your hands when you’re done (whether its Blue-White, or White-Blue).</p>
<p>It does matter which one you pick first though. But yeah, 4/15 = probability of going White-Blue. Blue-White would be 2/6*4/5 = 8/30 -> 4/15.</p>
<p>So its 8/15 total.</p>
<p>Or alternatively, find the prob of having just 2 whites and 2 blues, and subtract them from 1.</p>
<p>White-White prob is 4/6<em>3/5 = 12/30 or 6/15
Blue-Blue prob is 2/6</em>1/5 = 2/30 or 1/15</p>
<p>So its 7/15 of not having 1 White and 1 Blue, or 8/15 of having 1 White and 1 Blue.</p>
<p>Haha your right. Thanks for pointing it out. I guess thats what happens when you do these late at night :)</p>
<p>It’s an easy mistake to make and a very subtle point – one that I have NEVER seen tested on an SAT.</p>