Question

A football coach is trying to decide: When a team is ahead late in the game, which strategy is better?

Play the "regular" defense.

Play a "prevent" defense that guards against long gains but makes short gains easier.

The coach reviews the outcomes of 100 games.



Compare the probability of winning when playing regular defense with the probability of winning when playing prevents defense. Draw a conclusion based on your results.

Answer 1

Answer: The probability of winning when playing regular defense is higher than the probability of winning with *prevent* defence.

Explanation:

Let us assume that a total of 100 games were reviewed, 50 games were using regular defense method while the remaining 50 games were using the prevent defense method.

Out of the 50 regular defense games, 38 were win while 12 games were lose.

Out of 50 prevent defense game, 29 were win, while 21 games were lose.

The Probability of winning by regular defense is:

P(win by regular) = 38/50 = 0.76

Probability of winning by playing prevent defense is:

P(win by prevent) = 29/50 = 0.58

From the above analysis we observe that the probability of winning by using the regular defense method is greater than the probability of winning by prevent defense method.

That is 0.76 > 0.58.

Therefore, the team is more likely to win by using the regular defense method.

Answer 2

You are more likely to win by playing regular defense.

Explanation:

Assume out of 100 reviewed games, there were 50 regular defense games and 50 prevent defense games. And out of 50 regular defense games, 38 were win, 12 were lose. And out of 50 prevent defense game, 29 were win, 21 were lose.

Probability to win the game by playing regular defense is:

P(win | regular) = 38/50 = 0.76

Probability to win the game by playing prevent defense is:

P(win | prevent) = 29/50 = 0.58

Since the probability of winning by regular defense game is more than prevent defense game (0.76 > 0.58), you are more likely to win by playing regular defense.