Question

2 Sasha believes her soccer team plays better at away games than at home games. Her team played 12 games at home and 12 games away. She recorded the wins over this season. Based on these results, what is the probability for home and away wins? Is she right about her team playing better away? Show your work. Place: Home Away

Answer 1

Explanation:

To calculate the probability of home and away wins, we need to know how many wins the team had at home and away, respectively.

Let's assume that the team won x games at home and y games away, where x and y are unknown variables. Then we know that:

x + y = total number of wins (which we'll denote as W)

x + (12 - y) = 12 (the number of home games)

(12 - x) + y = 12 (the number of away games)

Solving these equations for x and y, we get:

x = (W + 12) / 2 - 12

y = (W + 12) / 2 - 12

Now, let's say the team won 8 games in total. Then, using the equations above, we can calculate that:

x = 2 (i.e., they won 2 games at home)

y = 6 (i.e., they won 6 games away)

Therefore, the probability of a home win is 2/12 = 1/6, and the probability of an away win is 6/12 = 1/2.

Based on these calculations, Sasha is correct in her belief that the team plays better away. The probability of an away win is higher than the probability of a home win.