Probability Homework #1

I'm back! Tonight I did some of my probability math homework and it wasn't too horrible. The funny thing though is I sat down and was like okay math homework, prepare to be solved! I opened to my first question and got stumped on that one for almost 20 minutes! :( What a great start! I did eventually solve it, so no worries. I did find one question from my homework that very interesting and actually fun to do.

The question said I had a container with seven letters in it. The letters where TRACKED, yes I know they spell tracked. Now my math homework wanted me to find the probability of the outcome being TRACE, in that order, if I drew a letter one by one without replacing it. So, the probability of drawing the first letter in TRACE, if there are seven letters in the container, is 1 out of 7. After drawing the first letter and not replacing it, the probability of drawing the next letter correctly is 1 out of 6. As you continue the probability of drawing the third letter correctly is 1 out of 5, the fourth letter correctly 1 out of 4, and the fifth letter correctly 1 out of 3. After the fifth draw you stop because TRACE only has five letters in it. Each time you draw another letter, the sample space decreases by one. Once you have all of your probabilities, you multiple them together:
                            (1/7)(1/6)(1/5)(1/4)(1/3)
 
All that multiplication comes out to be 1 out of  2520, which is the probability of drawing TRACE. Pretty simple in the end but interesting if you really think it through.

That's all for today. Have a great Thursday everyone (at least it's almost Friday)! :)

Lauren  

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 Probability Day #2!

Today was our second day learning probability and let me tell you that at some points my brain was spinning, hence the title of my blog. We started out with a card activity, pretty tame. We were asked questions like what is the probability of drawing a red card from the deck. We solved this question by first determining how many cards are in a deck: 52. We then asked ourselves how many suits are in a deck: 4 (diamonds, hearts, clubs, and spades) and how many of those suits are red: 2 (diamonds and hearts). So, 26 out of 52 cards are red, or one half. We had other questions like what is the probability of drawing not a queen from the deck. First we had to figure out how many queens are in a deck of cards: 4 (one diamond, one heart, one club, and one spade). Since the question asked what is the probability of not drawing a queen, we subtracted the four queens from the total number of cards which was 52. So, 48 out of 52 or 12 out of 13 (after reduced) were not queens.

The next activity we did in class involved cute little black and white pom poms. Don't let the cute part throw you off, they were vicious! Anyway, with this activity we were given questions that told us we had a box that contained three white pom poms and two black pom poms. A pom pom would be drawn from the box at random and not replaced. Then a second pom pom was to be drawn from the box and not replaced. We needed to draw a tree diagram and find all possible outcomes.  So, with the first draw we could get a white pom pom or a black pom pom. The probability of pulling a white pom pom was 3 out of 5 and the probability of pulling a black pom pom was 2 out of 5 (5 being the total number of pom poms in the box). Next, we had to make a second draw. Now remember we already pulled a pom pom from the box and didn't replace it, so the total number of pom poms will change. So, lets say we pulled a white pom pom from the box on our first draw. When we draw for the second time, we still have the possibility of pulling a white or black pom pom again. The probability of pulling a white pom pom would be 2 out of 4 because there is a total of four pom poms in the box after you drew the first one and didn't replace it. And since we said the first pom pom we drew was white, then there are only two white pom poms left in the box. The probability of pulling a black pom pom would also be 2 out of 4 because there are a total of four pom poms and since we didn't pull a black pom pom on our first draw, the two original black pom poms are still in the box. The same process applies if you were to draw a black pom pom on your first draw instead of a white pom pom. The numbers would be slightly different.       

Click here for an example of a tree diagram of flipping a coin.

So to say the least, it was a big day in math class. Some things I was able to grasp pretty easily, while other things I struggled with and will need more practice on. But hey, that's where math homework comes in handy. I hope your head isn't spinning too bad......until next time! :)

Lauren  

  

Introduction!

This....is my very first blog! 

So, if there are mistakes bare with me. This is my first blog post for my math class (157) and I am excited to see what is in store! :)

Probability Day #1!

On Monday we started our unit of probability. We did an activity that was called Healthy Fish. Everyone in the class paired up with a partner and we were suppose to be given bags of multicolored goldfish, but the bags of goldfish were nowhere to be found. So, we had to pretend. By the way, if your reading my post and your the one who stole the bags of goldfish, we're coming to get you! Anyways, our teacher, Mrs. Klassen, handed out a worksheet that we were to fill out as we did the activity. Each group was given and x amount of healthy fish and an x amount of unhealthy fish for our pretend pond. In my group we had 82 healthy fish and 8 unhealthy fish. Next, Mrs. Klassen let us solve the questions on our worksheet on our own. This was a great way for us to be active while learning. Some of the problems/questions that we had to solve were "compute the probability that a fish in your pond is healthy." "Unhealthy." My group found that the probability of having a healthy fish in our pond was 82:90. 82 being the number of healthy fish that we were given and 90 being the total number of fish in our pond (82+8). We did the same process to compute the probability of the unhealthy fish. healthy unhealthy
  
After the activity we talked about some math vocabulary that we needed to know for the unit. The three vocabulary words that I found most interesting were Equally Likely, Impossible Event and Certain Event. They are all pretty self explanatory and straight forward. Equally likely is when the outcomes or results of an experiment are likely as one another. Impossible event is something that will never happen. An example would be pulling a tiger or giraffe out of the pond. Certain event is something that will happen. An example of that would be that you will always pull a fish out of the pond. 

It was a fun filled day in math class! More blog posts to come, stay tuned! :)

For laughs and giggles: Click here

Lauren