<p>Type of Chocolate Bar / Percent cocoa by weight
Milk / 35
Dark / 50
Bittersweet / 70</p>
<p>A website sells three types of chocolate bars of equal weight. If Serena orders two chocolate bars at random from the website, then melts them together, what is the probability that the resulting mix contains at least 50 percent cocoa by weight?</p>
<p>The answer is 1/2, but I don't know how they got that.</p>
<p>Well, first consider all the scenarios. The question does not restrict Serena from purchasing two of the same kind of chocolate bar.</p>
<p>Serena can order milk & milk, milk & dark, milk & bittersweet, dark & dark, dark & bittersweet, and finally bittersweet & bittersweet. So, there are 6 possible combinations.</p>
<p>Now, calculate the %age of cocoa in the mixtures.
Milk & Milk gives (35+35)/2 = 35%
Milk & Dark gives (35+50)/2 = 42.5%
Milk & Bittersweet gives (35+70)/2 = 52.5%
Dark & Dark gives (50+50)/2 = 50%
Dark & Bittersweet gives (50+70)/2 = 60%
Bittersweet & Bittersweet gives (70+70)/2 = 70%</p>
<p>Redwood, this is section 9, #16 Princeton review 11 tests book, right? i thought the back said it was 4/9 aka c.
i don't have the book anymore (library), so please post the question and the explanation. that'll help</p>
<p>p.s. liarliar, your way of calculating % cocoa is wrong. you cannot average because the chocolate bars are of different weight</p>
<p>D-Yu - I'm confused by your statement. As written, the question says "A website sells three types of chocolate bars of equal weight." Am I missing something here?</p>
<p>Either way, I'm sure you'll do great on the SAT! I'm not a college applicant, just a tutor who stumbled across this board. Good luck to everyone taking the SATs!</p>
<p>The proability of each bar being either dark or bittersweet is 2/3, so the probability that they are both dark or bittersweet is 2/3 x 2/3 = 4/9</p>
<p>That is where the 4/9 comes from (its in the explanation)</p>
<p>Lol, just curious, how did u remember this exact question</p>
<p>And yes, I posted the exact question word for word, and it says the bars are of equal weight.</p>
<p>i did this very test coupla days ago before i had to return the book. I kept my score sheet
OK, an alternate solution for the 4/9 is this:
imagine 9 total possiblities : 3 choices for the 1st chocolate bar multiplied by 3 choices for the 2nd chocolate bar.
As liar liar pointed out, there are 4 ways of getting a more than 50% cocoa
milk - bittersweet, bittersweet-bittersweet, bittersweet-dark, dark-dark.</p>
<p>PR's explanation is weird, cuz it says you have to have dark or bittersweet, but according to the posts, you can get >50% w/ milk and bittersweet
idk, tho'. I'll wait until I get the book back, and then post what i think</p>
<p>The probability of drawing milk the first time is 1/3. P(M) = 1/3
The probability of drawing dark the first time is 1/3. P(D) = 1/3
The probability of drawing bittersweet the first time is 1/3. P(B) = 1/3</p>
<p>When milk is drawn first, overall cocoa content is 50% or more only when bittersweet is drawn second (the possibility of which is 1/3). So P(M) x P(B) = 1/3 x 1/3 = 1/9.
When dark is drawn first, overall cocoa content is 50% or more only when dark or bittersweet is drawn second (the possibility of which is 2/3). So P(M) x P(D union B) = 1/3 x (1/3 + 1/3) = 1/3 x 2/3 = 2/9.
When bittersweet is drawn first, cocoa content is 50% or more only when bittersweet is drawn second (the possibility of which is 1/3). So P(B) x P(B) = 1/3 x 1/3 = 1/9.</p>
<p>1/9 + 2/9 + 1/9 = 4/9.</p>
<p>PR's explanation is correct because you cannot have 50% or more without drawing dark or bittersweet at least once. I think this is a conditional probability question. I didn't think the question all the way through before because I was stuck on the original poster's statement that the correct answer was 1/2. Still, no excuse. Good job redwood and D-Yu.</p>
<p>the problem does not state that the chocolate bars are of equal weight. If you look at the table, each chocolate bar weighs differently. Therefore, there are only 4 ways to get over 50% - dark-dark, dark-bitter, bitter-bitter, and bitter-dark (order matters I guess). answer is 4/9</p>