Question

The probability that the engine in your car fails is 0.002. Insurance on engine repairs costs $200, and pays out $4000 in the case of failure. Construct a probability distribution for your earnings. Find your expected earnings.

Answer 1

Step-by-step explanation:idek

Answer 2

The Solution:

Given:

`\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}`

Required:

To construct a probability distribution for your earnings. hence, find your expected earnings.

Step 1:

The probability distribution is:

Recall:

`4000-200=3800`

Step 2:

The expected earnings is:

`\sum_{i\mathop{=}1}^2x_iP(x_i)=3800(0.002)+200(0.998)=7.6+199.6=207.2=\text{ \$207.2}`

Therefore, the correct answer is $207.20