On any given day, a salesman can earn $0 with a 45% probability, $250 with a 25% probability, or $400 with a 30% probability. His expected earnings equal: $ nothing (round your answer to the nearest penny).
Accepted Solution
A:
Answer: $ 182.5Step-by-step explanation:The expected value of occurring events [tex]x_1,\ x_2, \ x_3\ ....,x_n[/tex] having probabilities [tex]p_1,\ p_2,\ p_3\ ....,p_n[/tex] is given by :-[tex]E(x)=x_1\cdot \ p_1+x_2\cdot \ p_2+x_3\cdot \ p_3+....+x_n\cdot \ p_n[/tex]Given : On any given day, a salesman can earn $0 with a 45% probability, $250 with a 25% probability, or $400 with a 30% probability.i.e. Probability of earning $0 = 0.45Probability of earning $250=0.25Probability of earning $400=0.30Then , the expected earnings is given by :-[tex]E(x)=0\times0.45+250\times0.25+400\times0.30=182.5[/tex]Hence, the his expected earnings is $182.5.