Question

An amusement park owner tracked the ages of visitors who frequented different rides and displayed the data in a table.


Teacups Ferris Wheel Gondola Ride Roller Coaster
Under 12 33 7 14 16
12 – 25 20 8 28 7
Over 25 12 17 19 9
Is being under the age of 12 independent of riding the roller coaster at this amusement park? Justify the conclusion mathematically.
No, because 0.062 = (0.368)(0.168)
Yes, because 0.062 = (0.368)(0.168)
No, because 0.084 ≠ (0.368)(0.168)
Yes, because 0.084 ≠ (0.368)(0.168)

Answer 1

To determine whether being under the age of 12 is independent of riding the roller coaster at the amusement park, we need to calculate the probability of a visitor being under 12 and riding the roller coaster, and compare it to the probability of a visitor riding the roller coaster regardless of age.

The probability of a visitor being under 12 and riding the roller coaster is 16/120 or 0.133.

The probability of a visitor riding the roller coaster regardless of age is (16+7+9)/120 or 0.35.

Since 0.133 is not equal to 0.368 times 0.168 (the probabilities of being under 12 and riding the roller coaster and being under 12, respectively), we can conclude that being under the age of 12 is not independent of riding the roller coaster at the amusement park. Therefore, the correct option is (c) No, because 0.084 ≠ (0.368)(0.168).