# Thread: A certain experiment is to be performed until a successful result is obtained.

1. ## A certain experiment is to be performed until a successful result is obtained.

Im not sure what distribution method to use here.
Over all though im not sure what to do here..

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 dollars; however, if a failure results, it costs 5000 dollars 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?

2. ## Re: A certain experiment is to be performed until a successful result is obtained. Originally Posted by jesseschnup Im not sure what distribution method to use here.
Over all though im not sure what to do here..

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?
reposted with escaped dollar signs

3. ## Re: A certain experiment is to be performed until a successful result is obtained. Originally Posted by jesseschnup Im not sure what distribution method to use here.
Over all though im not sure what to do here..

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?

Successful trials will be distributed as a geometric distribution

a)

$p_k=P[\text{success on kth trial}] = (0.25)(0.75)^{k-1},~k\geq 1$

the cost of success on the $kth$ trial is

$C_k = (25000)k + (5000)(k-1)= 30000k-5000$

\$25000 for all the trials that were necessary and \$5000 to set up after the $(k-1)$ failed trials

so the expected cost is

$E = \displaystyle \sum_{k=1}^\infty C_k p_k$

and I leave it to you to determine this

b) first determine how many trials can be run

$n \ni 30000n - 5000 \leq 200000$

then determine

$\displaystyle \sum_{k=1}^n~p_k$

This is the probability the experimenter will have enough money.

So take 1 minus this for the probability that they won't have enough money

c) you should have enough info now to complete this, yell back if not.

4. ## Re: A certain experiment is to be performed until a successful result is obtained.

Ah thank you for taking time out of your day to help.
This is just what i need to get the ball rolling,

just so im getting this right -

so there are an expected cost of failures ((1/.25) - 1) * 5000 to get 15000 then add 25000 to get the last success to get Expected cost of 40,000

or is it 30000 for failures because of the fact that you have to setup if the last was a failure so 25000+5000 = 30000 cost of the failure

5. ## Re: A certain experiment is to be performed until a successful result is obtained. Originally Posted by jesseschnup 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 dollars; however, if a failure results, it costs 5000 dollars to
"set up" for the next trial. It is believed that the probability of
success on a single trial is 0.25.
a) What is the expected cost of the experiment?
This a very well know problem. Look at this page.
In case the expected number of trials is $\dfrac{1}{.25}$.
I leave it to you to do that arithmetic.

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