Question

The Manchester United football (soccer) team is a perennial power in the English Premier League. Their 2017 season was a little unusual because they had 15 draws (ties) in their 38 matches. The two-way table summarizes the association between location and outcome. Suppose we select one game at random. using this chart.

a. What is the probability that they won the game?
b. What is the probability that they didn't win the game?
c. What is the probability that they were playing at home and won the
game?
d. What is the probability that they were playing at home or won the game?

Answer 1

a. Probability of winning (P(won)) = 18/38

b. Probability of not winning (P(didn't win)) = (38 - 18)/38

c. Probability of playing at home and winning (P(home and won)) = 10/38

d. Probability of playing at home or winning (P(home or won)) = 27/38

The Breakdown

a. The probability that Manchester United won the game is given by the number of wins divided by the total number of matches:

Probability of winning (P(won)) = 18/38

b. The probability that Manchester United didn't win the game (includes both losses and draws) is given by the number of non-wins divided by the total number of matches:

Probability of not winning (P(didn't win)) = (38 - 18)/38 = 20/38

c. The probability that Manchester United was playing at home and won the game is given by the number of home wins divided by the total number of matches:

Probability of playing at home and winning (P(home and won)) = 10/38

d. The probability that Manchester United was either playing at home or won the game can be calculated using the addition rule for probabilities:

Probability of playing at home or winning (P(home or won)) = (19 + 18 - 10)/38 = 27/38