The cost of a trial conducted in the research and development center of an industrial establishment is known to be 1 million dolars. If the test is negative, in addition to this a new trial is required, which would cost additional 300 thousand dolars. Trials are independent from each other and the probability of success of each trial is 0.2. Calculate the total cost of the projects until the first successful attempt occur.
Asked
Active
Viewed 34 times
0
-
Welcome to Mathematics! For these kinds of problems, it is customary to note where you got them from, what you understand about the problem, as well as what you've tried. That way we can provide the right level of help. – Ken May 19 '15 at 17:59
-
1The total cost is a random variable $X$. You probably want to know the mean of $X$. If that is the case, please modify your question accordingly. Also, please indicate what you have tried so that one may help you deal with the source of difficulty. Are you familiar with the geometric distribution? – André Nicolas May 19 '15 at 18:00
-
I tried the binomial solving but I did'nt understand the solution and your comments? – user241915 May 19 '15 at 18:35
1 Answers
0
The expected value is
$1000000×0.2+1300000×0.8×0.2+1600000×0.8^2×0.2+1900000×0.8^3×0.2+…$
$=1000000×0.2(1+0.8+0.8^2+0.8^3+…)+300000×0.8×0.2(1+2×0.8+3×0.8^2+…)$
The sum is broken into two parts: one with $1000000$ and one with $300000$. Could you use these two identities: $$1+r+r^2+...=\frac{1}{1-r}\text{ and } 1+2r+3r^2+...=\frac{1}{(1-r)^2}, 0\leq r < 1$$ to solve the problem?
James Pak
- 1,547