Probability difficultities
Message posted by Tara Ryan (via 152.163.207.181) on May 28, 2001 at 9:18 PM (ET)

Hi,
My name is Tara Ryan and I am currently taking a Probability and Statistics class. I was given a homework assignment over the holiday weekend, and I came across a few questions. Since the school is closed, I thought I'd look else where for some help.

Given 2 events a and b of a sample space such that p(a)=.2, p(b)= .4 and p(a I b) + p( b I a) = 0.75. Find p( a and b)

like i said in my last email i already know that p(a I b) can equal p(a) * p(b I a). but i do not see how to combine them to have them both equal 0.75.

2)Approximately 10% of the bottles coming off a production line have serious flaws in the bottle. If six bottles are randomly selected from the production line,
1) what is the probabilty that exactly 2 will have serious flaws/
( this is how i think you would go about solving the problem

p(bottles with flaws)
n = 6
p(2) = p(y < 2) - p(y < 1)
= .930 - .730
)
2) what is the probability that less than or equal 2 bottles have serious flaws in the sample?
(again, this is how i think the problem should be solved

p(1 < x < 6) = p(y < 6) - p(y < 0) or p(2) = 1 - p(y < 2)
= 1.00 - .349 = 1 - .930

3)The manager of a stockroom in a factory has constructed the following probability distribution for the daily demand (number of times used) for a particular tool.

Y 0 1 2 3
___________________________________
p(y) .1 .3 .5 .1

i) find the mean number of times the tool is used.
i think 1/4 ( but this does not seem right)

ii) If it costs the factory $10.00 each time it is used, what is the mean cost of the daily cost for the use of the tool.

iii) what is the variance of the daily cost for the use of the tool?

4) LAST ONE.....I SWEAR

There are 8 candidates seeking to become president of the United States. Let the candidates be represented with the letters, A, B, C, D, E, F, G, H.
=> Candidates D, E, F have the same chance of winning.
=> Candidates G and H have no chance of winning.
=> Candidate A is three times likely to be selected as candidate B and B is two time likely to be elected as C.
=>Candidate D is one third likely to win the election as C.

a) what is the probability that C will win the election?

b) What is the probability that A will NOT win the election?

READERS RESPOND:
(In chronological order. Most recent at the bottom.)

Re: Probability difficultities
Message posted by Phil (via 66.32.19.202) on May 29, 2001 at 3:07 AM (ET)

Just few hints:

2. Use the Poisson Distribution

3. Expectation

4. Total probability = 1.