Determine whether rolling a 6-sided number cube is a good way to answer a 20-question multiple-choice test if there are 6 choices for each question. Justify your answer.
Mr. D is picking teams for volleyball in gym by having the students count off by 2's. The 1's will be on one team and the 2's on the other. Would flipping a coin would work just as well to pick the teams? Justify your answer.
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So, for the first part, you have a 1 in 6 chance of randomly rolling for the correct number. Do this 20 times. (1/6)^20 is your chance to get a 100%.
if you use random chance to answer multiple choice you can only expect to get 1 in 6 answers correct that is about 16.7%
If you want a specific grade, you will need to use the binomial equation.
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Mr D.s method will ensure that no two people in counting order are on the same team, with a coin toss there is an even chance that people in counting order will be on the same team
For the second part, you need to think about what can happen when flipping a coin. You COULD end up with everyone on the same team. If you make the assumption that there are limits, and that there is no preferential standing order, then flipping a coin is just as good. Since these are not given, however, flipping a coin does not guarantee an even number of people on each team.
ah , good point Vandreigan, i hadn't thought of that
Good old statistics and probability. Always some little thing to trip you up :D
lol.. i agree with you.. and of courze, MANY thanks to you... and of course @UnkleRhaukus!
Lilai3, have you covered the binomial equation in your class? For part 1, you can calculate the probability of a passing grade, if you have that equation. Otherwise, just realize that getting a perfect score has a very low probability.
what's binomial equation (r middle skoolers allowed to be here)?
Ah, no, you likely haven't covered it. It's an equation that can be used to calculate the probability of a set number of things happening given a set number of chances, regardless of order. You likely won't run into it until high school at the earliest!
Good luck, and don't overcomplicate the problems. Think carefully and you'll be just fine!