All Seats On A Plane Are Numbered So Passengers Are Assign

All Seats On a Plane Are Numbered So That Passengers Are Assigned A Se

All seats on a plane are numbered so that passengers are assigned a seat. The layout is as follows: The rows are numbered from 1 to 30. In each row, there are 6 seats, 3 on each side of the aisle, labeled from A to F. Each row has 2 window seats.

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Calculate the total number of seats on the plane, the probability of not sitting in row 7, the probability of sitting in a window seat, the probability of sitting in an "A" seat, and the probability of sitting in an even-numbered row.

Analysis and Solution

Total Number of Seats on the Plane

Given the airplane has 30 rows, with 6 seats per row (labeled A through F):

Total seats = Number of rows × seats per row = 30 × 6 = 180 seats.

Probability of NOT Sitting in Row 7

Total seats in the entire plane: 180

Seats in row 7: 6

Seats not in row 7: 180 - 6 = 174

Probability of NOT sitting in row 7 = (Seats not in row 7) / (Total seats) = 174 / 180 = 29 / 30 ≈ 0.9667 or 96.67%.

Probability of Sitting in a Window Seat

Each row has 2 window seats. Total window seats = 30 rows × 2 = 60.

Total seats = 180.

Probability of sitting in a window seat = 60 / 180 = 1 / 3 ≈ 33.33%.

Probability of Sitting in an "A" Seat

In each row, there is 1 "A" seat, and there are 30 rows.

Total "A" seats = 30.

Probability = Number of "A" seats / Total seats = 30 / 180 = 1 / 6 ≈ 16.67%.

Probability of Sitting in an Even-Numbered Row

Number of even-numbered rows from 1 to 30: 2, 4, 6, ..., 30.

Count of even rows = 15.

Seats in each row: 6.

Total seats in even rows = 15 × 6 = 90.

Probability = Seats in even rows / Total seats = 90 / 180 = 1 / 2 = 50%.

Conclusion

The total number of seats on the plane is 180. The probability of not sitting in row 7 is approximately 96.67%. There's about a 33.33% chance of sitting in a window seat, a 16.67% chance of sitting in an "A" seat, and a 50% chance of sitting in an even-numbered row. These calculations help passengers understand their seating probabilities and preferences better and assist airlines in planning and optimization strategies.

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