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.
but before we get to the dread-inducing question a quick rundown.
the magical, make-your-life-a heck-of-a-lot-easier probability equation:
# of possibilities you are hoping to get
# of total possibilities
let’s take the formula out for a test drive.
i have a pouch with three red marbles and two blue marbles. what is the probability i grab a red marble?
the answer is 3 (since i’m hoping for the red marble when i dip my mitt into the pouch—and there are 3 red marbles).
the total number of marbles is 2 blue + 3 red = 5.
therefore, the probability of grabbing a red marble is 3/5.
now let’s make things slightly more complicated.
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?
using the formula for the white marble, i get 2/6, since there are two white marbles (what i’m 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—and not 6—total marbles. so there are 3 black marbles out of a total 5, or 3/5.
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.
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’t lost your marbles, you are ready for the challenge problem. good luck!
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%?
- 0
- 1
- 3
- 4
- 6
after working through the problem, get a full explanation here:
leave me any comments or questions you have below! 🙂
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