A certain experiment is to be performed until a successful result is obtained. T
ID: 2923179 • Letter: A
Question
A certain experiment is to be performed until a successful result is obtained. The trials are independent and the cost of performing each trial is $25,000; however, if a failure results, it costs $5000 to "set up" for the next trial. It is believed that the probability of success on a single trial is 0.25. Using appropriate probability model(s), ...
a) What is the expected cost of the experiment?
b) Suppose that the experimenter has a maximum of $200,000 available. Find the probability the experimenter does not have enough $ to run the experiment to completion.
c) In order for the probability of part b) to be reduced to 0.01 the success probability of each trial would need to be increased to what value?
Explanation / Answer
Answer to part a)
the expected cost of Success is 25000
its probability is 0.25
expected cost of failure is 25000+5000 for next trial = 30000
its probability = 0.75
.
Thus expected total cost = 25000*0.25 + 30000*0.75
expected total cost = 28750
.
Answer to part b)
each failure trial costs = 30000
Total available = 200000
We want the experiment not to finish , that means number of failures = 200000/30000 = 6.66 ~ 7
Thus Probability of experiment not complete = (0.75)^7 = 0.133484
.
Answer to part c)
in order to make the probability 0.01 instead of 0.133484 ,
x^7 ~ 0.01
x = 0.517947
This implies probability of failure that was earlier equal to 0.75 , must be reduced to 0.517947
This implies the probability of success must be equal to = 1 - 0.517947 = 0.482053
Thus th probability of success must be increased to 0.48
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.