Math Games

Archive for April, 2006

Question: How can i make a probability game for math class?

ok so in math class were talking about probability and for our end of the year project we have to make something that involves probability. I am in 7th grade. i dont really want to do a spinning wheel, dice, or a bean bag toss. those are what most people are doing. I don't want something that is complicated to make just something that will be cool and i can find out theoretical and experimental probability for.

Answer: Do the Monty Hall Game!

Here are the rules: there are 3 doors. Behind one is a sports car, behind the other two is a goat. Obviously the contestant wants to win the sports car. You could make little doors, and use a toy car and two toy animals.

The contestant picks a door. The host then opens a different door, revealing a goat. The contestant then has the choice of changing which door they pick. The question is: are your chance of winning better if you stay with your original choice, or if you change? (Or doesn't it matter).

If you repeat the experiment many times (say, with each member of the class), you should find:
- people that don't change have a 1/3 proability of winning
- people that do change have a 2/3 probability of winning

i.e. you're better off changing. This is a result that surprises many people, even adults. The reason, basically, is that your original pick had a 1/3 probability of being right, so (after one goat is revealed) the other door has a 2/3 probability of being right.

Math Video: Probability

Question: Trouble with a math reasoning problem?

Joseph drove from his house to the football game at an average rate of 50 miles per hour. Because of traffic jams, he drove home from the football game along the same route at an average rate of only 35 miles per hour. If his total driving time to the game and back from the game equaled 3 hours and 24 minutes, then how many total miles did he drive?

I understand the problem but I'm having trouble figuring out the answer. Please help and show your work.

Answer: The distance is the same in both directions. So, let's call the distance d.

To the game, he drove d miles at 50 miles per hour, so it took d/50 hours to get there. On the way home, it took d/35 hours.

24 minutes is 24/60 hours, or .4 hours, so 3 hours 24 minutes is 3.4 hours.

d/50 + d/35 = 3.4 Multiply by the LCM of 50 and 35, which is 350:

7d + 10d = 1190
17d = 1190
d = 70 miles

BUT d is the distance one way, so in total he drove 2d or 140 miles.

Love Games Ep. 1 5+ Comments For Marathon