Question

A construction company is considering submitting bids for two contracts. It

will cost the company $10,000 to prepare and submit the bids, and if won,
each bid would produce $50,000 of income to the company. The company
estimates that it has a 10% chance of winning any given bid.
Here is the probability distribution of X = the number of bids the
company wins, and M = the amount of money the company profits from
the bids.
X= # of bids won
M = profit
Probability
0
-$10,000
0.81
1
$40,000
0.18
bids
2
$90,000
0.01
Find the expected value of the number of bids won.
E(X)=

Answer 1

Explanation:

To find the expected value of the number of bids won, E(X), we need to multiply each value of X with its corresponding probability and then sum these products.

E(X) = (X1 * P1) + (X2 * P2) + (X3 * P3)

Here, X1 = 0, X2 = 1, X3 = 2, and their corresponding probabilities are P1 = 0.81, P2 = 0.18, and P3 = 0.01.

E(X) = (0 * 0.81) + (1 * 0.18) + (2 * 0.01)

E(X) = (0) + (0.18) + (0.02)

E(X) = 0.20

The expected value of the number of bids won is 0.20.