The first thing we did was make a correction in our dictionary notes, for an error was found. In the slide post for Tuesday, Febuary.27/07 under "combinations (the "choose" formula) heading. The slide currently says:
"A permutation is an ordered arrangement of objects"
We changed that to:
"A combination is an arrangement of objects were order does not matter."
Next we moved onto our "let's warm up" slide, this question ended up taking up most of the period. It was a question very similar to one we had done in a past class.
Question:
There is a 10 question multiple choice test, with four possible choices for each question. What is the probability of scoring at least 10% on the test if you guess each answer?
There are two ways to answer this question an easy way and a hard way.
*Method #1 (the long way)*
This is where you calculate the probability of getting each number of questions right on the test, 2/10, 3/10, 4/10, etc up to 10/10. When all 11 are added up the probabilities should equal 100%.
10! 1 ^0 3 ^10
_________ * { ___ } * { ___ } =0.563135147 =6%
(10!0!) 4 4
10! 1 ^1 3 ^9
_________ * { ___ } * { ___ } =0.1877117157 =18%
(9!1!) 4 4
10! 1 ^2 3 ^8
_________ * { ___ } * { ___ } =0.2815675735 =28%
(8!2!) 4 4
10! 1 ^3 3 ^7
_________ * { ___ } * { ___ } =0.2502822876 =25%
(7!3!) 4 4
10! 1 ^4 3 ^6
_________ * { ___ } * { ___ } =0.1459980011 =14%
(6!4!) 4 4
10! 1 ^5 3 ^5
_________ * { ___ } * { ___ } =0.0583992004 =6%
(5!5!) 4 4
10! 1 ^6 3 ^4
_________ * { ___ } * { ___ } =0.0162220001 =2%
(4!6!) 4 4
10! 1 ^7 3 ^3
_________ * { ___ } * { ___ } =0.0030899048
(3!7!) 4 4
10! 1 ^8 3 ^2
_________ * { ___ } * { ___ } =3.862380981E-4
(2!8!) 4 4
10! 1 ^9 3 ^1
_________ * { ___ } * { ___ } =2.861022949E-5
(1!9!) 4 4
*Method #2 (short cut)*
Solving for the "compliment" also known as the opposite.
10! 1 3
1 - __________ * {_____} * {_____}
(10! 0!) 4 4
3 ^10
= 1 - {_____}
4
=0.9437
=94.37%
This method works because the question is asking for the probability of getting at least 10%, so that means 1-10 questions right. So you calculate the probability of getting all the questions wrong, which leaves the probability of getting them all right.
This "compliment" method is not only less work but it takes up much less time. But if an individual was to use method #1 it would not be marked wrong. But in a timed event such as a test the "compliment" method would come in handy.
Next we got to a surprise quiz, we didn't get a chance to correct the whole thing, but we went over some must know guidelines to the first question.
*Reminder:
-All tree diagrams start with a dot, as a student already stated in past scribe.
-Also a legend is always something good to write down when solving a question with a tree diagram.
This is not something that needs to be done now, but later on it will be needed, and will help make your answers a lot easier to understand (read).
Example:
o=oatmeal
p=pancakes
Well ladies and gentlemen that's all for me, sorry it took while but here it is finally.
The scribe for Friday's class is/was Donna.
Bye bye
Brittany<3
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