A sporting goods manufacturer was asked to sponsor a local boy in two fishing tournaments. They claim the probability that he will win the first tournament is 0.4. If he wins the first tournament, they estimate the probability that he will also win the second is 0.2. They guess that if he loses the first tournament, the probability that he will win the second is 0.3.

a) According to their estimates, are the two tournaments independent? Explain your answer.

b) What’s the probability that he loses both tournaments?

c) What’s the probability he wins both tournaments?

d) Let random variable X be the number of tournaments he wins. Find the probability model for X.

e) What are the expected value and standard deviation of X?