Two-Way Table of Diners in Milton
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A survey was done in the town of Milton to see which diner people prefer most out of the three diners in town. The survey also asked whether the person usually ate out between 6 a.m. and 2 p.m., or between 2 p.m. and 10 p.m.
| 6 a.m. - 2 p.m. | 2 p.m. - 10 p.m. | Total | |
| Mary's Diner | 23 | 40 | 63 |
| Flo's Diner | 25 | 8 | 33 |
| Spoons Diner | 35 | 19 | 54 |
| Total | 83 | 67 | 150 |
A.
What is the probability that someone chosen randomly prefers Flo's Diner?
- 0.76
- 0.30
- 0.22
- 0.12
F.
Is going to Spoons Diner independent of eating out between 2 p.m. and 10 p.m.? Why or why not? There may be more than one correct answer.
- The probability that someone eats out between 2 p.m. and 10 p.m. is 0.45. The probability that someone likes Spoons, given that they eat out between 2 p.m. and 10 p.m. is 0.28. Because these are not equal, the two events are not independent.
- The probability that someone like's Spoons is 0.36, while the conditional probability that someone prefers Spoons given that they eat between 2 p.m. and 10 p.m. is 0.28. Since these are not equal, the events are not independent.
- The probability that someone eats out between 2 p.m. and 10 p.m. is 0.45. The conditional probability that someone eats out between 2 p.m. and 10 p.m. given that they prefer Spoons is 0.35. Since these are no equal, the events are not independent.
- Because the probability that someone prefers Spoons is 0.36, and this is almost equal to the conditional probability that someone eats out between 2 p.m. and 10 p.m. given that they like Spoons (which is 0.35), the events are independent.