SOLUTION: An event E has a probability p = p(E) = 0.4 in some sample space. Suppose the experiment that yields this sample space is repeated nine times and the outcomes are independent. Find

Algebra ->  Probability-and-statistics -> SOLUTION: An event E has a probability p = p(E) = 0.4 in some sample space. Suppose the experiment that yields this sample space is repeated nine times and the outcomes are independent. Find      Log On


   

Question 1204064: An event E has a probability p = p(E) = 0.4 in some sample space. Suppose the experiment that yields this sample space is repeated nine times and the outcomes are independent. Find the probability of getting the following outcome. (Round your answer to six decimal places.)
E exactly two times
Answer by ikleyn(52775) About Me  (Show Source):
You can put this solution on YOUR website!
.

It is a typical binomial distribution probability problem.


The number of trials is n= 9.
The probability of each individual trial success is p= 0.4.
The number of successful trials is 2 of 9.


Use the standard formula for probability

P = C%5B9%5D%5E2%2Ap%5E2%2A%281-p%29%5E%289-2%29 = 36%2A0.4%5E2%2A0.6%5E7 = 0.161243  (rounded).    ANSWER

Solved.

--------------------------

To see many other similar  (and different)  solved problems,  look into the lessons
    - Simple and simplest probability problems on Binomial distribution
    - Typical binomial distribution probability problems
in this site.

Learn the entire subject from there.


/////////////////


In this problem, the most unusual feature is the instruction to round to 6 decimal places.

I noticed that this instruction is copied in all your posts.

Let me tell you the truth: such instruction does not look reasonable.
It makes it clear that the creator copied it from problem to problem
without thinking, and it does not decorate this Math composer.