Your school's soccer team plays two games against another soccer team.The probability that your team wins the first game is 0.4.If your team wins the first game,the probability that they also win the second game is 0.4.If your team loses the first game,the probability that they win the second game is 0.3.Let the random variable X be the number of games won by your team.Find the expected value of X.
A)μ = 0.70
B)μ = 0.56
C)μ = 0.74
D)μ = 0.50
E)μ = 0.80

Question

Quizplus · Accepted Answer

We can use the formula for the expected value of a discrete random variable:

E(X) = Σ xi P(X=xi)

where xi is the value of the random variable and P(X=xi) is the probability of X taking on that value. In this case, X can take on values of 0, 1, or 2, representing the number of games won by your team.

P(X = 0) = P(loss first game) = 0.6
P(X=1) = P(win first game)P(win second game|win first game) + P(loss first game)P(win second game|loss first game) = 0.4x0.4 + 0.6x0.3 = 0.34
P(X=2) = P(win first game)P(win second game|win first game) = 0.4x0.4 = 0.16

So,

E(X) = 0x0.6 + 1x0.34 + 2x0.16 = 0.74

Therefore, the answer is C, μ=0.74.

Your School's Soccer Team Plays Two Games Against Another Soccer