Expert: Scott A Wilson - 9/3/2009

Question
Dear Scott,

Am really please to have a tutor like you !!
i have gone through with many illustrations you have mentioned over the site and found them quite easy to resolve now.

But my only problem is being a working student i hardly get time for my study and its been almost 6 years i am not in touch with Math at all.
But now for my MBA session i have to go through with it. Am finding problem with Statistics and Probability. Please help me to understand the basic of these topics so that i can resolve the base level question. I will be grateful to you.

If possible pls send me some notes or solved examples so that i can go through with it.

Will wait for your kind response
Thanks in Advance.

With Best Regards,
Geeta.

Answer
I need to know the question.  I will send some examples for you to look at, but there are even more problems that you will see.

Examples:

Question: The sum of all of the outcomes is 1.
Suppose a store has red, yellow, and blue balls.
The chance of a red ball is 0.40.  The chance of a yellow ball is 0.35.
What is the chance of a blue ball?

Answer: The chance is 1 minus the chances of the other two, so it is 1 - 0.4 - 0.35 = 0.25


Question: At a certain test in a high school, suppose that 10% of seniors fail and 20% of juniors fail.  There are 100 seniors and 120 juniors.  If a person fail, what is the chance of being a senior?

Answer: 10% of seniors fail, so that would be 10%(100) = 10.
20% of juniors fail, so that would be 20%(120) = 24.
That would mean that there would be around 10+24 = 34 people who failed, but only 10 are expected to be seniors.  This gives a chance of 10/34 = 5/17.


Question: The number of people on an airline has an average of 50 and a variance of 25.
What is the probability that there are more than 60 people?

Answer: We know that the standard deviation is the square root of the variance,
so the standard deviation is known to be 5.  Since the value being looked at is 60 and the average is 50, the amount that number is over the average is 60-50 = 10.
Since the standard deviation was 5, that's 2 standard deviation.
Looking up two on a one sided normal table gives us 0.9772.
This is the number that are less than 2 standard deviation.
Since we want the number over 2 standard deviations, that would be 1 - 0.9772 = 0.0228.

The table was http://www.math.unb.ca/~knight/utility/NormTble.htm


Question: The chance of a success if 0.8.
What is the probability of getting 3 succeses out of 5?

Answer: The chance of failure is 1 - chance of success = 1 - 0.8 = 0.2.
The binomial distribution is applied in this case.  It says that the chance of a success is
p(k) = (n choose k)(p^k)((1-p)^(n-k)) where n is the number of items, k is the number of successes, and p is the probability of a success.

Putting in the values gives (5 choose 3)(0.8^3)(0.2^2).

In the following, the ! is used for factorials.
2! = 2, 3! = 6, 4! = 24, 5! = 120; n! = n(n-1)(n-2)...3*2*1.
(a choose b) is defined to be a!/(b!(a-b)!).

It is known 5 choose 3 is 5!/(3!(5-3)!) = 120/(6*2) = 10.
It could also be said that 5*4*3*2*1/((3*2*1)(2*1)) is 5*4/(2*1) = 20/2 = 10.
It is known that 0.8^3 = 0.512.
It is known that 0.2^2 = 0.04.
Since the answer will be (5 choose 3)(0.8^3)(0.2^2), that is (10)(0.512)(0.04) = 0.2048.