The Solution:
Given:
[tex]\begin{gathered} P(car\text{ engine fails\rparen}=0.002 \\ \\ P(\text{ car engine does not fail\rparen}=1-0.002=0.998 \end{gathered}[/tex]Required:
To construct a probability distribution for your earnings. hence, find your expected earnings.
Step 1:
The probability distribution is:
Recall:
[tex]4000-200=3800[/tex]Step 2:
The expected earnings is:
[tex]\sum_{i\mathop{=}1}^2x_iP(x_i)=3800(0.002)+200(0.998)=7.6+199.6=207.2=\text{ \$207.2}[/tex]Therefore, the correct answer is $207.20
