Question

A company is deciding whether to fund research trials that, if successful, will earn the company some estimated profit. Suppose that each trial costs $50,000 and has a 20% success rate.

1. The company will keep funding the trials until it reaches the first success. What is the company’s expected cost and what is the standard deviation? (6 points)

2. What’s the probability that it will take three trials to reach the first success? (3 points)

Answer 1

Each trial costs $ 50,000 and success rate = 20%

Compay will keep funding the trials until it reaches the first success.

Here, if y is the cost of trials and x is the number of trials taken, then

x ~ GEOMETRIC(0.2)

p(x) = (0.80)x-1 * 0.2 ; x > 0

E[X] = 1/p = 1/0.2= 5

SD[X] = sqrt [(1-p)/p2] = sqrt [(1-0.2)/0.22] = 4.472

Here if y is the cost of the trial

then,

y = 50000 x

E[y] = 50000 * E[x] = 50000 * 5 = $ 250,000

SD[y] = 50000 * sqrt [4.4722]= $ 223606

P(IT will take three trials to get success) = P(No success in first two trials) * P(Sucess in third trial) = 0.8 * 0.8 * 0.2 = 0.128