You play two games against the same opponent The probability

You play two games against the same opponent. The probability you win the first game is 0.5. If you win the first game, the probability you also win the second is 0.3. If you lose the first game, the probability that you win the second is 0.1. Complete parts a) through e). Are the two games independent? Explain your answer. What\'s the probability you lose both games? What\'s the probability you win both games? Let random variable X be the number of games you win. Find the probability model for X. Find the expected value and standard deviation of X.

Solution

a)
No, the outcome of first determines the probability of    winnig the second game
b)
P( you loose the 1st game) = 0.5,P(second game you loose is) = 0.9
P( loose both the games) = 0.5*0.9 = 0.45
c)
P( win bth games) = 0.5*0.3 = 0.15
d)
X = 1, P( You win the 1st game & lose 2nd) + P( You lose the 1st & win d 2nd) = 0.5*0.7+0.5*0.1=0.40

X =0 , P(X) = 0.45
X = 1 , P(X) = 0.40
X = 2 , 0.15