Concept explainers
Making a First Down A first down is desirable in football—it guarantees four more plays by the team making it, assuming no score or turnover occurs in the plays. After getting a first down, a team can get another by advancing the ball at least 10 yards. During the four plays given by a first down, a team’s position will be indicated by a phrase such as “third and 4,” which means that the team has already had two of its four plays, and that 4 more yards are needed to get 10 yards necessary for another first down. An article in a management journal offers the following results for 189 games for a particular National Football League season. “Trials” represents the number of times a team tried to make a first down, given that it was currently playing either a third or a fourth down. Here, n represents the number of yards still needed for a first down. Source: Management Science.
n | Trials | Successes | Probability of Making First Down with n Yards to Go |
1 | 543 | 338 | |
2 | 327 | 186 | |
3 | 356 | 146 | |
4 | 302 | 97 | |
5 | 336 | 91 |
(a) Complete the table.
(b) Why is the sum of the answers in the table not equal to 1?
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Finite Mathematics (11th Edition)
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