Compute the probability, Mathematics

From past experience a machine is termed to be set up correctly on 90 percent of occasions.  If the machine is set up correctly then 95 percent of good parts are expected however if the machine is not set up correctly then the probability of a good part is only 30 percent.

On a specific day the machine is set up and the first component produced and found to be good.  What is the probability that the machine is set up appropriately.


This is shown in the form of a probability tree or diagram as given below:

2000_Compute the Probability.png

 Whereas: CS - Correct Setting

IS - Incorrect Setting

GP - Good Product

BP - Bad Product

P(CSGP) = 0.9 × 0.95 = 0.855

P(CSBP) = 0.9 × 0.05 = 0.045

P(ISGP) = 0.1 × 0.3 =   0.03

P(ISBP) = 0.1 × 0.7 =    0.07


- Probability of obtaining a good part (GP) = CSGP or ISGP

                                                            = CSGP + ISGP

                                                            = 0.855 + 0.03 = 0.885

Note: Good parts may be produced while the machine is correctly set up and when also it's incorrectly setup. In 1000 trials, 855 occasions while its correctly setup and good parts produced as CSGP and 30 occasions while its incorrectly setup and good parts produced as ISGP.

- Probability that the machine is correctly set up after getting a good part.

= number of favoural outcomes/total possible outcomes


= 0.855/ 0.885

= 0.966


= P (CS|GP)

= P (CSGP)/P(GP)

= 0.855/ 0.885

= 0.966

Posted Date: 2/20/2013 4:25:02 AM | Location : United States

Related Discussions:- Compute the probability, Assignment Help, Ask Question on Compute the probability, Get Answer, Expert's Help, Compute the probability Discussions

Write discussion on Compute the probability
Your posts are moderated
Related Questions
What is the OPEC? - The Organization of the Petroleum Exporting Countries, a coordination group of petrol producers The Organization for Peace and Economic Cooperation, a German le

Frequency Distribution or Variance Ratio Distribution This was developed by R. A Fisher in 1924 and is normally defined in terms of the ratio of the variances of two usually d

if x+y+z=pi=180 prove that sin^2x+sin^2y+sin^z-2sinx*siny*sinz=2

How did the teacher get 30 + 12 + 1.5 for the equation of volume of rectangular prism measuring L=14.4, W= 3, and H= 5? Formula given was V= Bh. My answer was x 3.

regression line drawn as Y=C+1075x, when x was 2, and y was 239, given that y intercept was 11. calculate the residual

Given: ??????? is supp. to ??????? ???? ????? bisects ??????? ???? ????? bisects ??????? Prove: ??????? is a rt. ?

Find the normalized differential equation which has {x, xex} as its fundamental set

If α & ß are the zeroes of the polynomial 2x 2 - 4x + 5, then find the value of a.α 2 + ß 2   b. 1/ α + 1/ ß  c. (α - ß) 2 d. 1/α 2 + 1/ß 2    e.  α 3 + ß 3 (Ans:-1, 4/5 ,-6,

Q. How to Subtract fractions involving negative numbers? Ans. This is the same as adding them, but just remember the rule that two negatives on the same fraction cancel ou

Q. Show Frequency Tables? Ans. A frequency table is used to show how often a piece of data occurs. Example: Michelle decides to keep track of the number of phone call