{"id":2347,"date":"2014-07-14t22:55:34","date_gmt":"2014-07-14t22:55:34","guid":{"rendered":"\/\/www.catharsisit.com\/sat\/?p=2347"},"modified":"2015-04-14t21:37:55","modified_gmt":"2015-04-14t21:37:55","slug":"probability-challenge-question-dont-lose-your-marbles-2","status":"publish","type":"post","link":"\/\/www.catharsisit.com\/hs\/sat\/probability-challenge-question-dont-lose-your-marbles-2\/","title":{"rendered":"probability challenge question: don’t lose your marbles"},"content":{"rendered":"

probability strikes dread into almost everybody. couple that with the fact that many probability questions are convoluted word problems so that even the most confident math-o-phile is quaking in her boots. <\/p>\n

but before we get to the dread-inducing question a quick rundown. <\/p>\n

the magical, make-your-life-a heck-of-a-lot-easier probability equation: <\/p>\n

# of possibilities you are hoping to get<\/u>
\n# of total possibilities <\/p>\n

let\u2019s take the formula out for a test drive.
\n<\/p>\n

i have a pouch with three red marbles and two blue marbles. what is the probability i grab a red marble?<\/em><\/p><\/blockquote>\n

the answer is 3 (since i\u2019m hoping for the red marble when i dip my mitt into the pouch\u2014and there are 3 red marbles). <\/p>\n

the total number of marbles is 2 blue + 3 red = 5. <\/p>\n

therefore, the probability of grabbing a red marble is 3\/5. <\/p>\n

now let\u2019s make things slightly more complicated. <\/p>\n

i have a pouch with 2 white marbles, 3 black marbles, and a blue marble. what is the probability i grab one white marble and then, without replacing the marble, grab a black marble?<\/em><\/p><\/blockquote>\n

using the formula for the white marble, i get 2\/6, since there are two white marbles (what i\u2019m looking for) and six total marbles. next, i want to apply the same math with the black marble, except i want to make sure that i remember there are now 5\u2014and not 6\u2014total marbles. so there are 3 black marbles out of a total 5, or 3\/5. <\/p>\n

next, whenever i have separate events in probability, i want to multiply. the separate events in this case are 1) grabbing a white marble and 2) grabbing a black marble. <\/p>\n

so i get 2\/6, which can be reduced to 1\/3 times 3\/5: 1\/3 x 3\/5 = 1\/5. if you are still with me, meaning you haven\u2019t lost your marbles, you are ready for the challenge problem. good luck! <\/p>\n

a marble pouch contains 4 blue marbles, 6 brown marbles, and 3 golden marbles. what is the fewest number of brown marbles that i need to remove from the pouch to ensure that the odds of reaching in and grabbing a golden marble are greater than 50%?<\/p>\n

    \n
  1. 0<\/li>\n
  2. 1<\/li>\n
  3. 3<\/li>\n
  4. 4<\/li>\n
  5. 6<\/li>\n<\/ol>\n

    after working through the problem, get a full explanation here:
    \n