Question

hree percent of all cars manufactured at a large auto company are lemons. Suppose two cars are selected at random from the production line of this company. Let x denote the number of lemons in this sample. Write the probability distribution of x.

Answer 1

Answer: The probability distribution of X

$\begin{tabular}{ X |P(X)|} X & P(X) & \\ 0 & .94& \\ 1 & .0582 & \\ 2 & .009 & \\ \end{tabular}\end{document}$

Step-by-step explanation:

Given

The probability of cars manufactured at a large auto company are lemons = $\frac{3}{100}$  = .03

The probability of cars manufactured at a large auto company are  (not lemons) other cars = 1 - .03 = .97

Two cars are selected randomly from the production line of this company

Let X denote the number of lemons in this sample

(1)  when both cars are not lemons =

P(x = 0)  = $.97\times.97$ = 0.94

(2) When first car lemon and second car not lemon or  When first car  not lemon and second car  lemon = P(x = 1)  = $.03\times.97 + .97\times.03$ = 0.0582

(3) when both cars are  lemons = P(x = 2) = $.03\times.03$ = .009