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	0	1	2
probability	0.81	0.18	0.01

find the expected value of the number of bids won.

( e(x) = ) bids

show calculator

Explanation:

Step1: Recall the formula for expected value

The formula for the expected value \(E(X)\) of a discrete random variable is \(E(X)=\sum_{i}x_ip_i\), where \(x_i\) are the possible values of the random variable and \(p_i\) are their corresponding probabilities.

Step2: Substitute the values into the formula

For \(x = 0\), \(p=0.81\); for \(x = 1\), \(p = 0.18\); for \(x=2\), \(p=0.01\).

$$
LATEXBLOCK0
$$

Step3: Calculate the sum

\(E(X)=0.18 + 0.02=0.2\)

Answer:

\(0.2\) bids