Your firm is considering the introduction of a new toothpaste. At a strategy session, it is agreed that a marketing study will be successful with probability 0.65. It is also agreed that the probability of a successful product launch is 0.40. However, given that the marketing study is successful, the probability of a successful product launch is 0.55.
a. Draw the appropriate probability tree for this situation.
b. Find the probability that the marketing study is successful and the product launch is successful.
c. Given that the product launch succeeds, find the conditional probability that the marketing study was favorable.
d. Find the conditional probability that the product launch is successful, given that the marketing study was not successful.
e. Are the two events "marketing study successful" and "product launch successful" independent? How do you know?