Monday, May 30, 2011
Sunday, May 29, 2011
Friday, May 27, 2011
Probability
Probability Ex. 39, 40, 41
Probability is the measure of how an event is. In other words,
P (A) = n(A) ® Probability = Number of Favorable outcomes
n Total Possible Outcomes
Probability of event A is the number of ways event A can happen, divided by the total possible outcomes.
Sample Space is the complete set of all possible outcomes.
Ex. Rolling a die, the sample space would be 1,2,3,4,5,6
Sample Spaces can be represented using tree diagrams or charts.
Addition Law (Or)
When 2 events, A and B are mutually exclusive. The probability that A or B will take place is the sum of both events.
P (A or B) = P (A) + P (B)
Ex. A single 6-sided die is rolled. What is the probability of rolling a 2 or a 5?
P (2) | = | 1 |
6 |
P(5) | = | 1 |
6 |
P(2 or 5) | = | P (2) | + | P (5) |
= | 1 | + | 1 |
6 | 6 |
= | 2 |
6 |
1 | |
3 Mutually Exclusive- if the occurrence of one will mean that the other will not occur
(Cannot have 2 events taking place at the same time). Mutually exclusive events
add up to one (complement).
Ex. Venn Diagram, the circles do not overlap  Non-Mutually
Exclusive-
if they have one or more outcomes in common  Independent events - If the result of the first draw/event does not affect the outcome of
the second draw/events. Ex. Event A – Drawing a card
from a deck. Then returning the card in the deck. Event B – Drawing from the
very same cards. Dependent Events- when you don’t replace the first item before drawing the second item. Ex. What is the probability of
getting a face card and then an Ace without replacing the face card? P (Face) = 12/52 P (Ace after Face) = 4/51 (12/52)(4/51) = 4/221 Multiplication Law (And) When 2 events, A and B are
dependent and influence one another.
You
would read P (B|A) as “the probability of B given A has already occurred”, also
known as, conditional probability.
Ex. A jar contains black and white marbles. Two
marbles are chosen without replacement. The probability of selecting a black
marble and then a white marble is 0.34, and the probability of selecting a
black marble on the first draw is 0.47. What is the probability of selecting a
white marble on the second draw, given that the first marble drawn was black?
P (A&B) = P (A)P (B|A) P (White|Black) =
P(Black
and White) = 0.34 P(black) 0.47 = 72%
Thanks Blaine! |
Thursday, May 26, 2011
Probability and Let's Make a Deal....
The Let's Make a Deal Dilemma
Investigate the Let's Make a Deal Paradox. This paradox is related to a popular television show in the 1970's. In the show, a contestant was given a choice of three doors of which one contained a prize. The other two doors contained gag gifts like a chicken or a donkey. After the contestant chose an initial door, the host of the show then revealed an empty door among the two unchosen doors, and asks the contestant if he or she would like to switch to the other unchosen door. The question is should the contestant switch. Do the odds of winning increase by switching to the remaining door?
Sunday, May 22, 2011
Fountain Parabolas
Just came across a wonderful blogspot: http://mathtourist.blogspot.com
This is Ivars Peterson's blogspot and he posts about anything in the world that catches his eye and is related to math and computer science. Check out his blogspot for more real world mathematical connections. Enjoy!
Thank you Mr.Peterson for your sharp eye and for providing the relevant, real life visual connections to mathematics.
This is Ivars Peterson's blogspot and he posts about anything in the world that catches his eye and is related to math and computer science. Check out his blogspot for more real world mathematical connections. Enjoy!
Thank you Mr.Peterson for your sharp eye and for providing the relevant, real life visual connections to mathematics.
Fountain Parabolas
Shooting graceful arcs of water into the air, fountains can offer lessons in geometric spectacle. The fountain at the National Gallery of Art Sculpture Garden in Washington, D.C., is a notable example.
Friday, May 20, 2011
Grade 12 Jimmies: You are Invited.....
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Tuesday, May 17, 2011
Hello,
So today I will blog about circles and ellipses.
First Circles ,I hope we all know what circles are, but if not circles can be defined as a set of points that are a given distance from a given point. The general equation of a circle is (x-h)^2+(y-k)^2=r^2. H and K is the center of the circle, remember that the H and K value are the opposite sign so if a given circle was located at (-3,4) it would read (x+3) and (y-4). The radius or R, is the distance from the center to any point on the circle. It is important to remember that when given an equation the R value must be square-rooted because it had been squared when R was put in to the equation. For example, if a given equation was (x+1)^2+(y-2)=16, then the radius would be 4 because the square root of 16 is 4.
Next is ellipses, ellipses are similar to circles except that not all points on the ellipses are equal distance from the center (there is no radius). The equation is (x-h)^2/a^2 + (y-k)^2/b^2. Again H and K are the center of the ellipse. 'A' represents the horizontal distance from the center, and B represents the vertical distance from the center. Remember again that H and K are the opposite signs of what is in the equation. An easy way to remember if the ellipses is horizontal or vertical is if; A greater than B than it is horizontal, and B is greater than A then it is vertical. You may notice that if the value of A and B are the same, then the equation turns into the circle equation. That being said if A and B are the same it forms a circle. This
is the case because a circle is actually a special case of an ellipses.
Ellipses are actually all over the place! Planets orbit in an elliptical way, the electrons also move elliptically around the nucleus. Have you ever heard of whispering galleries? This is when you whisper in one focal point in a building and at another focal point across the room you can hear the person as though they are standing right beside you, this occurs because the building is an ellipse.
Thank you for your time,
KG
Monday, May 16, 2011
More on Hyperbolas...
Lesson 2 B Conics
Lesson 3 Conics
For students looking for the Permutations & Combinations Quiz corrections from this morning, they will be posted in Edmodo.
Lesson 3 Conics
For students looking for the Permutations & Combinations Quiz corrections from this morning, they will be posted in Edmodo.
Friday, May 13, 2011
What does a Sonic Boom have to do with Hyperbolas?
A sonic boom shock wave has the shape of a cone, and it intersects the ground in part of a hyperbola. It hits every point on this curve at the same time, so that people in different places along the curve on the ground hear it at the same time. Because the airplane is moving forward, the hyperbolic curve moves forward and eventually the boom can be heard by everyone in its path.
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