Probability

Hi guys!! Sorry for the late post. Anyways here’s what we did in the last day of school before our winter break.
Our morning class start off with the story of Chicken Little. Here’s a link of the original story of Chicken Little.
Anyways after Chicken Little’s story Mr. K asked us this question:

What is the probability that the sky will fall?

He asked us to keep our answers to ourselves, meaning no talking o the people beside, behind or in front of us. Then after a few minutes he asked each of us our answers. Here are the answers given by us:

5/6
1/∞
0/1
0/0
1/10^100
0/0.5
1/6
1/0
1/1000000
1/12
15/100


And as you can see, some of us answered 0/0 and 1/0. Actually I was one of those people who said it for some unexplainable reason. But then he showed us this link explaining why these can’t be the answer to his question(Dr. Math). It explained why cant 0 be the denominator because 0 represents to the number of things could happen and if we have 0, this means there is 0 number of thing that could happen. Mr K told that to us by freezing because if there 0 number of thing that can only happen then we can’t move. For further explanations for this topic about 0/0 and 1/0 being wrong please go to the posted link. Thank you.

Anyways the correct answer 0/some big number.

Then Mr. K told us these vocabularies:

Probability: the branch of mathematics that deals with chance.
Sample Space (Ω): the set of all possible outcomes for a given
"Experiment" represented by capital omega Ω.
Event (E): A subset of the sample space. A particular occurance in a given
experiment.
Simple Event: The result of an experiment that is carried out in a single
step.
Example: Flip a coin. The result is heads
(a simple event)
Compound Event: The result of an experiment carried out in two (or
more) steps.
Example: 1. Flip a coin and roll a die - 6 .The result is {H,6}
Example 2: Flip a coin twice. The result is {H,T}
Certain Event: an event whose probability is 1
Example: roll a die - 6 and get a result less than 10
Impossible Event: an event whose probability is 0.
Example: roll a die - 6 and get a 7
Complimentary Event: the compliment of E is E':
If P(E) = a then P(E') = 1-a
Example: Given a standard deck of cards, a card is drawn at random.
P(spade) = (13/52) = (1/4)
P (not a spade) = 1 - (1/4) = (3/4)

Probability can be expressed as:
- A ratio
- A fraction
- A decimal
- A percent

And this formula helps expressing probability.



Important Note: PROBABILITY OF AN EVENT IS ALWAYS BETWEEN 0 AND 1

Now we know the basics of probability, it’s time for examples. Here are the examples Mr. K gave us.

~~Determine the sample space when a fair die is rolled.

Answer: 1, 2, 3,4,5,6 are the possible outcome when we roll a die. These numbers are the sample space. Sample space is the list of all the possible outcome of an event.

~~Determine the sample space for rolling die and flipping a coin.

Answer:



H1...H6 and T1...T6 are the sample space because these are the possible outcome for this event.

**notice the similarity to counting. A table or a tree diagram can help determine the sample space.

~~Determine the probability of rolling a 2 when rolling a fair die.

Answer: 1/6

It is because in a fair die you only have one 2 so out of the six numbers in the die, the possibility we will get 2 is one. So 1 is our numerator and 6 is the denominator because overall these are all the number that we could get including 2.

~~Determine the probability of getting a head and an odd number when rolling a die and flipping a coin.

Using the chart we made earlier we can determine answer



The probability is 3/12 or ¼.
It is because out of the 12 possible answer (h1-h6,t1-t6) the one with head and is an odd number are h1, h3, and h5. So these 3 numbers are our answers out of the 12 possible answers.

Those are the semi easy questions now here comes a next level type.

~~~~A bus is scheduled to arrive at a train station at any time between 07:05 and
07:15 inclusive. A train is scheduled to arrive between 07:11 and 07:17 inclusive. The arrival of a bus at 7:06 and a train at 07:14 can be represented by the ordered pair (6, 14). Times are expressed in whole minutes.

a) Sketch a sample space for this event (use a chart).
b) How many ordered pairs are there in this sample space?
c) How many ordered pairs have the bus and the train arriving at the same time?
d) How many ordered pairs have the train arriving after the bus?
e) What is the probability of the bus arriving after the train?

Bus time are 5...15 (horizontal)
Train time are 11...17 (vertical)



Answer

B) 77
C) 5 ordered pairs have the same number. In other words the bus and train arriving time is the same.
D) 62 ordered pairs have the first number less than the second. In other words the bus arrives first than the train.
E) 10/77 is the probability that the train arrive first before the train.


Sigh* I’m finally over. Well I think I covered everything about probability. After our probability lesson in our afternoon class Mr K told us about TED. It’s like a conference for brilliant and I would say wealthy people. And it’s interesting especially the math magician person I forgot how he called himself but he was awesome. He can calculate things faster than a calculator I guess. He was so good. He’s awesome I could say. Anyways that’s all I have to say. Sorry for the late post, I tried using the smartboard thing but it made my computer froze and run slower so I decided to use this method. Uhmm if I missed anything just message me or something so I can fix it. Sigh* finally I’m done, the next scribe will be MICHELLEs.

Have a safe and fun winter break guys and Merry Christmas!!