Football Strategies A particular football team is known to run 30% of its plays to the left and 70% to the right. A linebacker on an opposing team notes that the right guard shifts his stance most of the time (80%) when plays go to the right and that he uses a balanced stance the remainder of the time. When plays go to the left, the guard takes a balanced stance 90% of the time and the shift stance the remaining 10%. On a particular play, the linebacker notes that the guard takes a balanced stance.

a. What is the probability that the play will go to the left?

b. What is the probability that the play will go to the right?

c. If you were the linebacker, which direction would you prepare to defend if you saw the balanced stance?

a) 0.659

b) 0.341

c) It'll be smarter to prepare to defend the left hand side as the probability of play going through that side when the right guard takes a balanced stance is almost double of the probability that the play would go through the right when the right guard takes a balanced stance.

Step-by-step explanation:

Considering the left first

Play goes through the left 30% of the time

- The right guard takes a balanced stance 90% of the time when play goes through the left, that is, 0.9 × 0.3 = 27% overall.

- He takes a shift stance 10% of the time that play goes through the left = 0.1 × 0.3 = 3% overall.

Play goes through the right, 70% of the time.

- He takes a balanced stance 20% of the time that play goes through the right, that is, 0.7 × 0.2 = 14% overall

- He takes a shift stance 80% of the time that play goes through the right, that is, 0.7 × 0.8 = 56% overall.

Then the right guard takes a balanced stance 27% + 14% of all the time = 41% overall.

a) Probability that play goes through the left with the right guard in a balanced stance = 27/41 = 0.659

b) Probability that play goes through the right with the right guard in a balanced stance = 14/41 = 0.341

c) It'll be smarter to prepare to defend the left hand side as the probability of play going through that side when the right guard takes a balanced stance is almost double of the probability that the play would go through the right when the right guard takes a balanced stance.