91Ó°ÊÓ

Let's define the events. Event A is that the first car selected is a lemon and Event B that the second car is a lemon. Since the selection of the first car does not remotely affect the chance of the second car being a lemon (as the company makes a very large number of cars, and the sample size is just two cars), the events are independent.

The probability of a car being a lemon (Events A and B) is 0.05 or 5% and the probability of it not being a lemon is 0.95 or 95%.

The probability distribution list all possible outcomes of 'x' the number of lemons, and its associated probability. There are 3 outcomes when selecting two cars: \n- 0 Lemon: The probability is the product of the probabilities that both cars are not lemons which is calculated by \(P(A' \cap B') = P(A') \times P(B') = 0.95^2 = 0.9025\). \n- 1 Lemon: The probability is the sum of the probabilities that exactly one of the two cars is a lemon. Since our two events (first and second pick) are similar and independent, this is calculated by \(2 \times P(A \cap B') = 2 \times P(A) \times P(B') = 2 \times 0.05 \times 0.95 = 0.095\). \n- 2 Lemons: The probability that both cars are lemons is calculated by \(P(A \cap B) = P(A) \times P(B) = 0.05^2 = 0.0025.\)

In a tree diagram, each possible event is represented as a branch starting from the initial point (selection of the first car) to the final possibilities (the outcome of the second car). The probability of each event is written along its corresponding branch. Calculate and represent all the potential outcomes: no lemons, one lemon and two lemons. Remember that since these are independent events, we multiply the probabilities of each event along the branches to get the combined event probability.