Answer to Question #264241 in Statistics and Probability for Emily

Question

A car salesperson is scheduled to see two clients today. She sells only two models of car, an executive ( ) E and a basic ( ) B model. Each executive model sold earns the salesperson a commission of N$ 2000, while each basic model sold earns her only N$1000. If the sale is lost ( ) L , no commission is earned. Suppose P E( ) 0.2 = , P B( ) 0.3 = , and P L( ) 0.5 = , and that the sales are independent of each other. Let the random variable X be the total commission earned by the salesperson today. What values can X take on?

Answer 1

Lets reprsent what outputs may be and calculate probabilities and total comission:

both cars E (0.2*0.2=0.04) commision: 2*2000=4000

1 - E, 2 - B (0.2*0.3=0.06) commision: 2000+1000=3000

1 - E, 2 - L (0.2*0.5=0.1) commision: 2000+0=2000

Both cars B (0.3*0.3=0.09) commision: 2*1000=2000

1 - B, 2 - E (0.06) commision: 3000

1 - B, 2 - L (0.3*0.5=0.15) commision: 1000+0=1000

Both cars L (0.5*0.5=0.25) commision: 0+0=0

1 - L, 2 - E (0.1) commision: 2000

1 - L, 2 - B (0.15) commision: 1000

So, X can take on next values (in $): 4000, 3000, 2000, 1000, 0