$T371 Practice Midterm 1 Fall 2017 Use the following for questions 11-13: There
ID: 3277466 • Letter: #
Question
$T371 Practice Midterm 1 Fall 2017 Use the following for questions 11-13: There are three outcomes for soccer teams playing in an international soccer game: a win (W). a loss (L), or a tie (T). Suppose the US men's soccer team plays in two international soccer games with the following probabilities for each game: P(w) 0.5, PtL)-0.3, PT) 0.2. Assume the outcomes of the two games are independent. 11. (10 points) List all possible outcomes for the US men's soccer team from the two games, e.g., WL denotes that the team wins the first game but loses the second, and calculate the probability of each outcome. 12. (10 points) What is the probability that the US men's soccer team wins at least 1 game? 13. (10 points) Suppose the US men's soccer team receives 3 points for a game win, 1 point for a tie, and 0 point for a loss. How many points can the US men's soccer team expect to receive from the two games?Explanation / Answer
11) All the possible outcomes in the 2 games would be represented as:
Here W represents a win, L represents a Lose and T represents Tie.
{ WW, WL, WT, LW, LL, LT, TW, TL, TT }
Therefore there are a total of 9 outcomes here.
12) Probability that the US men's soccer team wins at least one game. This could be there in one of the following cases:
Therefore the total probability of at least one win is computed as the sum of all above probabilities.
= 0.15 + 0.1 + 0.25 + 0.15 + 0.1 = 0.75
Therefore 0.75 is the required probability here.
13) The expected number of points in the 2 games could be computed as:
The expected value of the number of points could be computed as:
= 0.15*3 + 0.1*4 + 0.25*6 + 0.09*0 + 0.06*1 + 0.15*3 + 0.06*1 + 0.04*2 + 0.10*4
= 0.45 + 0.4 + 1.5 + 0 + 0.06 + 0.45 + 0.06 + 0.08 + 0.4
= 3.4
Therefore 3.4 is the expected number of points here.
Case Probability P(X) Points P(X) WL 0.15 3 WT 0.10 4 WW 0.25 6 LL 0.09 0 LT 0.06 1 LW 0.15 3 TL 0.06 1 TT 0.04 2 TW 0.10 4Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.