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Monday, May 08, 2006

Scribe ? Whos' Next ?

So it's finally my turn to be scribe. Hmm.. this could be my last time being scribe before the exam too. The probability of that happening is very high as there seems to be a lot of people left for scribing so not only do I have to do a GREAT scribe and dethrown manny but also finish the year with a BANG! Anyway on to the scribe.

Today we only had a single class which began with the usual, Mr. K finishing his lunch while writing questions on the board.

1) A Pre-cal 40S studen takes a 20 question multiple choice test with four possible answers to each question. If she knows the answers to 12 of the problems, what is the probability of her scoring 90% on the test by guessing on the remaining questions ?

Well to start this question off we know that there are 8 questions remaining in the test, and in order for her to gain a 90% she MUST answer any of the next six questions right. The 'word' that we create with that information would be as follows : RRRRRRWW; were the R represents a right answer and the W representing a wrong answer. The catch towards this is assuming that she gets the next 6 questions right and the last 2 wrong, but having six right and two wrong can happen in many different ways, therefore we use the choice formula to figure out how many different ways it can happen :

8C6 = 8! / 6!2!

The eight is the number of questions remaining while the 6 is the number of questions she must answer right and the 2 is the number of questions she is allowed to be wrong.

Back to the word : RRRRRRWW

Since we also know the student has 1/4 chance of getting the question right and 3/4 getting a question wrong. It is 1/4 to get an answer right because there are four possible solutions to a question and only one is right our of three and visa versa for wrong answers.

From that and the word we know notice that her chances of getting 6 questions right is (1/4)
6
and her chances of getting 2 questions wrong is (3/4)2

If we take the number of combinations she could get 6 right and 2 wrong (8C6) and the number of times she can get 6 right ((1/4)6) and the number of time she can get 2 wrong ((3/4)2), and multiply it all together we get the probablilty she will get 90% on her test :

8C6(1/4)6(3/4)2
= 28 (1/4096)(9/16)
= 0.38 %

2) A piggy bank contains 2 quarters, 3 dimes and 5 nickels. When you turn it over and shake it any coin can fall out. What is the probability of shaking out two coins that total more than 30 cents ?




Explainations are all on the image itself, if still confused feel free to leave a comment and either me or someone else will elaborate for you.








3) A family has 5 children. If the birth of a boy or girl is equally likely, what is the probability that the family consists of
a) Exactly 2 girls
b) at least 2 girls

a) For this half of the question, is exactly like the first question I had explained. First we find the number of combinations for 2 girls, 5C2. The 5 from the number of children and the 2 from then number of girls you want. From there you then see what the ratio from girl to boy is which is (1/2)2 to (1/2)3. The 1/22 is the probability of the number of girls and the 1/23 is the probability of boys. Then we just multiply together like before :

5C2(1/2)2 (1/2)3
= 10 (1/4) ( 1/8)
= 10 ( 1/32)
= 10 / 32
= 31.25 %

b) This question is easier done by finding the compliment. The compliment of having at least 2 girls is having 5 boys or 4 boys and 1 girl.

5 Boys :
P(oG) = 5! / 5! (1/2)5
= 1 / 32

P(1G) = 5!/4!(1/2)4(1/2)1
= 5 / 32

With the answers from the compliemtn we then subtract one from the sum of the compliment.

P(At least 2G) = 1 - (1/32 + 5/32)
= 1- (6/32)
= 32/32 - 6/32
= 26/32
=81.25%

From there we got grouped together to work on a worksheet. Unfortunately we only had time to do the first question. I do not remember what the question was as Mark took it with him but I remember some of it.

7 girls and 2 boys sitting at a round table. what is the probability of the 2 boys sitting together ?

7!2!/8!
= 2/8
= 1/4

The 7! is from the number of combinations you can arrange the girls, and the 2! is the number of combinations you can arrange the boys. The 8! is the total number of possibilities of both sexes. Notice how the total number of possibilities is 8! not 9!, this is because we are dealing with a circle here. One person has to be the reference point as they can sit anywhere therefore we subtract one as earlier discribed in an earlier scribe.

FINALLY done, three hours of work whoa. VERY frustrated as blogger decided to delete my other finished scribe, and when I clicked on recover post it just recovered my draft *curse you. Very annoyed about that wow I sound mad and yeah I am but i'll let it steam out.

BTW Charlene, it's all yours tomorrow ;P



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3 Comments:

At 5/09/2006 8:05 PM, Blogger Cheryl Oakes said...

Well, I really enjoyed reading your reflection, SCRIBE. I too have written in blogger and lost most of the writing. So..... now,here is a teachable moment, I usually do my writing in a word document, then when done with the post, I select, copy and paste into Blogger. Since, then I haven't lost a thing. Oh, yeah, it took me more than a couple times of losing information before I began writing my posts in word. Over and out. Mrs. Oakes

 
At 5/10/2006 7:30 AM, Blogger Mr. H said...

Nice post. Annoying when blogger blogs down on you. All the detail in explaining the work is excellent. It is a little plain though (losing a previous version could be a reason. With a little editing and adding a few more diagrams this would be hall of fame worthy.

An excellent explanation

Mr. Harbeck

 
At 5/12/2006 7:32 PM, Blogger Lani said...

Hi Abriel,

Great introduction, using probability as your lead in to your post!!!

Thanks for your clear explanations!

I've always found that "technology gremlins" do their best to confound us when we're working the hardest, at least they do with me. I always tell people never take it personally, and do just as you did, blow them away with excellence!

Best,
Lani

 

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