The accompanying table shows the frequencies that a football

The accompanying table shows the frequencies that a football team called a running play or a passing play for various down and distance situations for the first five games of a season. Complete parts a) through f) below. a) What is the probability that the team will pass the ball on any given down?

nothing

(Round to three decimal places as needed.)

b) What is the probability that the team will run the ball and it is second down?

nothing

Down and distance

Run

Pass

1st down and 10 or more yards to go

56

81

2nd down and 6 or more yards to go

28

51

2nd down and 5 or less yards to go

19

9

3rd down and 2 or more yards to go

2

60

3rd down and 1 yard to go

1

4

(Round to three decimal places as needed.)

c) What is the probability that the team will pass the ball, given that it is 3rd down and they have 1 yard to go?

nothing

(Round to three decimal places as needed.)

d) What is the probability that the team will run the ball and it is 1st down?

nothing

(Round to three decimal places as needed.)

e) What is the probability that the team will run the ball, given that it is 2nd down and they have 6 or more yards to go?

nothing

(Round to three decimal places as needed.)

Solution

Consider:

a)

P(pass) = 205/311 = 0.659163987 [ANSWER]

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b)

P(run|2nd down) = (28+19)/(79+28) = 0.439252336 [ANSWER]

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c)

P(pass|3rd down, 1 yard) = 4/5 = 0.8 [ANSWER]

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d)

P(run|first down) = 56/(56+81) = 0.408759124 [ANSWER]

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e)

P(run|2nd down, 6 yards) = 28/(28+51) = 0.35443038 [ANSWER]