<p>Here is my question: </p>
<p>Type of chocolate bar Percent cocoa by weight
Milk 35
Dark 50
Bittersweet 70</p>
<p>A website sells 3 types of chocolate bars of equal weight. If Serena orders 2 chocolate bars at random form the website, the melts them together, what is the probability that the resulting mix contains at least 50% cocoa by weight?
A. 1/9
B. 1/3
C. 4/9
D. 1/2
E. 2/3</p>
<p>I dont understand why the answer is D.
I'd be grateful if you guys give me some help !
thanks so much.</p>
<p>who told you the answer is D? It isn't</p>
<p>i'll try to go through this step by step - my math is getting rusty a year out of school.</p>
<p>Probability is defined as: (number of times a particular result happens)/(total possible kinds of results) * 1.</p>
<p>Since 2 chocolate bars are picked out at random from among 3 types, the total possible kinds of results = 3*3 = 9.</p>
<p>So Serene could get 1 of 9 different mixtures of chocolates.:</p>
<p>MM
MD
MB
DM
DD
DB
BM
BD
BB</p>
<p>To calculate % cocoa in the resulting mixture, simply take the average of the two initial cocoa %s.</p>
<p>The only mixtures that don't give at least 50% cocoa are MM, MD and DM.</p>
<p>So 6 out of 9 possible mixtures give at least 50% cocoa. 6/9 = 2/3.</p>
<p>Answer is E, but could some check this please. And if anyone cld find a simpler and more elegant solution, please post it, I can't think well, I'm sleepy.</p>
<p>The answer is E.</p>
<p>here are 6 possible ways she can purchase 2 bars:</p>
<p>Milk, Milk
Milk, Dark
Milk, Bittersweet
Dark, Dark
Dark, Bittersweet
Bittersweet, Bittersweet</p>
<p>Of those 6, the first 2 don't work, but the other 4 do.</p>
<p>4/6 =2/3</p>
<p>This question is from Princeton Review's 11 tests book. The answer is D,actually. But the explanation is weird, and doesn't make sense.</p>
<p>If anyone has some more reasonable solutions to that one, please post them here.
Thankx so much.</p>