Question

You play two games against the same opponent. The probability you win the first game is 0.8. If you win the first game, the probability you also win the second is 0.6. If you lose the first game, the probability that you win the second is 0.4. Complete parts a) through e). a) Are the two games independent? Explain your answer A. Yes; all events are independent. O B. No; the outcome of the first game determines the probability of winning the second game. ° C. Yes; the outcome of the first game has no impact on the second game. 0 D. No; no events are independent. b) What's the probability you lose both games? o ! (Type an integer or a decimal.) c) What's the probability you win both games? Type an integer or a decimal.) d) Let random variable X be the number of games you win. Find the probability model for X P(x) e) Find the expected value and standard deviation of X E(X)= (Type an integer or a decimal.) (Round to three decimal places as needed.)

Answer 1

a)
Option B

b)
Probability of losing both games = (1-0.8)*(1-0.4) = 0.12

c)
probability of winning both games = 0.8*0.6 = 0.48

d)
P(X = 0) = 0.12
P(X = 1) = 0.8*0.4 + 0.2*0.4 = 0.4
P(X = 2) = 0.48

e)
E(X) = 0*0.12 + 1*0.4 + 2*0.48 = 1.36

Var(X) = (0 - 1.36)^2*0.12 + (1 - 1.36)^2*0.4 + (2 - 1.36)^2*0.48
= 0.4704

SD(X) = sqrt(0.4704) = 0.686