You play two games against the same opponent. The probability you win the first game is 0.4. If you win the first game, the probability you also win the second one is 0.2. If you lose the first game, the probability that you win the second game is 0.3.

a. Are the two games independent?
b. What's the probability you lose both games?
c. What's the probability you win both games?
d. Let random variable X be the number of games you win. Find the probability model for X complete the table below (hint: use your answers in part b and c)
X
P(x)
0
1
2
e. Find and interpret the expected value of X?
f. What is the standard deviation of X?