Is anyone else out there struggling with the probability unit. My students seem to shut down. Not sure why. Thoughts?
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Probability
Probability
Re: Probability
I did a lot of gambling with my students, whenever possible making it about cards and dice, and bringing out a deck. We played Texas hold 'em, and then did simple things like calculating the probability that you could get your straight on the river etc. You have to be careful in that there are a lot of things that are fairly complex to calculate (at least for me anyway).
For the perms and combs we always talked in terms of the class (I had a class of 5 so it was easy, but you could easily just use a subset of the class) when it was possible. At the beginning, we actually formed all possible permutations (with 4 kids) and combinations using kids standing up and running around to get in order.
My kids seemed to enjoy probability, maybe because I told them it could actually be useful to them in life when they win the world poker tour or go bet at the racetrack. Or if you want to be a goody-two-shoes about it you can use it to explain why you shouldn't gamble at the casino (I still talk about experimental vs. theoretical probability) as a good way to talk about odds and probability.
Re: Probability
Terri
Can you share some of these activities with us. I am very interested in trying to make my class more interactive.
Re: Probability
In response to your questions, and in line with a few others:
I generally start by keeping things really simple.
We take out a deck of cards make sure that we all see there are 52 cards, 4 suits, and 13 of each suit.
Then we talk about the probability of picking a red card, then a 7 etc.
I usually have a student actually pick a card. I find this is a good time to discuss theoretical vs. experimental probability. Like they have a 1/4 probability of picking a diamond. So have them pick 4 cards with replacement and see if they get 1 diamond. You can do all sorts of simple little things like this until they get it.
I really drill into them the fact that if something is guaranteed to happen the probability is 1, and if it's guaranteed not to happen the prob. is 0. I do some old fashioned stuff, like marching around the room repeating stuff, but the kids laugh and usually remember.
I also have them roll dice a lot. We make a tally chart with the numbers 2 to 12 and go to about 100 rolls with 2 dice. It usually works out quite nicely, but you can always explain differences with experimental vs. theoretical.
All this stuff is pretty basic (some kids said they did it in grade 7?), but I find it useful to ground them in the concepts and make sure they get the idea that it's favourable outcomes/total possible outcomes.
Re: Probability
My students also struggled a lot with Probability. I think it was mostly because many of them didn't know when to use a straight fraction (desirable outcomes/possible outcomes) and when to use factorials, when to use permutations, when to use combinations, when to use sets etc.
I even found that students were making really weird mistakes like having a probability answer be, for example, 7. An answer that really makes no sense as I had reiterated many times that a probability had to be between 0 and 1 (or 0% and 100%).
A lot of it is weak reading skills as well. Not reading carefully or not understanding the question made Probability a difficult unit for my students.
Re: Probability
My kids struggled as well. I think it was because they just did not understand what probability was. Second time through, I plan on spending more time with basic probability...what it is, simple examples (one step) before starting two step
Re: Probability
I have reached the permutations and combinations section for probability, and it seems to me like all of a sudden we are dealing with some types of problems we never approached much prior to this in the Perms and Combos chapter, or else I just can't remember them. If anyone has some clarification, I don't have an answer key for my materials, and these questions were bugging me (its one of those frazzled days!).
1) Mike's MP3 player contains 50 songs. If he listens to 10 songs on "random", determine the probability that the playlist contains:
a) Mike's two favorite songs
b) One of his favorite at the beginning of the 10 songs and the other at the end.
2. A hacker is attempting to break into a friend's security-protected file. The friend tells the hacker all the numbers that are in the 4-digit PIN but not the order or how many times the digit may be repeated in the PIN. Determine the probability that the hacker correctly guesses the 4-digit PIN on the first attempt if the friend tells her that the PIN contains:
b) only the numbers 4,5,and 6
c) only the numbers 4 and 5
Re: Probability
Let me attempt to tacle #1 for you!
Probability in #1 is (total favorable outcomes)/(total # of outcomes)
#1a) is a very tricky question because in order to come up with the number of favorable outcomes we need to choose the songs (Comb) and then arrange them (Perm).
The total number of ways to choose 10 songs from 50 so that his 2 favorite songs are included is: (2 C 2)(48 C 8). Because the 10 songs can be in any order we multiply that by (10 P 10) or 10!
The total number of ways to arrange any 10 songs given 50 is (50 P 10)
So our answer which is (total favorable)/(total) is [(2 C 2)(48 C 8)(10!)] / (50 P 10)]
Sorry i dont have a graphing calc with me so not sure what works out to!
#1b. Mike's 2 favorite songs have to be chosen leaving us with 8 more to choose from 48. The number of favorable outcomes in this case will be (48 P 8)(2!). We can use (48 P 8) this time because the 8 chosen songs stay together and are not influenced by his favorite at the beginning and the end. The 2! is because there are 2 ways to arrange his favorite songs at the beginning and end.
The total number of arrangements is again 50 P 10 so our answer should be:
(48 P 8)(2!) / (50 P 10)
Re: Probability
I just thought I'd throw this out there, but any questions that involve both Permutations AND Combinations are beyond the curriculum for 30-2.
I find my kids had enough difficulties with the types of questions that are in the curriculum, so I don't try to "challenge" them with things they don't need to know.