statistics help

Question

A small software company bids on two contracts. It anticipates a profit of $30,000 if it gets the larger contract and a profit of $15,000 if it gets the smaller contract. The company estimates that there is a 34% chance it will get the larger contract and a 55% chance it will get the smaller contract. If the company does not get either contract, it will neither gain nor lose money. Assuming the contracts will be awarded independently, whats the expected profit?

Answer 1

For expected value, you obtain this value by finding the sum of all the probabilities of each event multiplied by the value of the event.

 

The formula for expected value is:
Expected value = [P(A) * A] + [P(B) * B] + ... + [P(N) * N]

where P(A) + P(B) + ... + P(N) = 1.

So the expected profit would be:
Expected profit =[ P($30,000) * $30,000 ] +[ P($15,000) * $15,000 ] + [P($0) * $0 ]
= [ .34 * $30,000 ] + [ .55 * $15,000 ] + [ (1 - .34 - .55) * $0 ]

= $10,200 + $8,250 + $0

= $18,450.

 

As you can see, P($0) is obtained by finding the probability that the other events not happening, which would be

1 - P($30,000) - P($15,000)