a software company bids on two contracts simultaneously it a

a software company bids on two contracts simultaneously. it anticipates a profit of $120,000 on the larger contract and a profit of $75,000 on the smaller contract. The company estimates there is a 30% chance it will get the larger contract. There is a 70% chance that the company will also win the smaller contract if it wins the larger contract. The company estimates that there is a 60% chance that it will get the smaller contract if it did not get the larger contract. Find the company\'s expected profit and its standard deviation.

Solution

Thus there are 4 possibilities

Expected value of profit = sum of prob x profit

=[ 0.3(120000)+0.7(75000)+0.333(75000)]/2

= 36000+17500+25000/2

= 39225

For variance first find out E(X^2)

= 1/4[0.3(120000)^2+0.7(75000)^2+0.333(75000)^2]

= 1000000/4[4320+1312.5+1875]

= 1876875000

Var(x) = 1876875000-39225²

= 338274375

STd dev = 18392.23