A boutique coffee house tracks the monthly habits of its 120 loyalty card holders. The frequency of their visits and their preferred beverage type are summarized in the table below.
| Monthly visits, vvv | Espresso-based | Filter coffee |
|---|---|---|
| v<10v < 10v<10 | 18 | 32 |
| 10≤v<2010 \le v < 2010≤v<20 | 22 | 18 |
| v≥20v \ge 20v≥20 | 14 | 16 |
One of the 120 members is selected at random.
Find the probability that the member prefers Filter coffee.
Given that the member visits fewer than 10 times a month, find the probability that this member prefers Espresso-based drinks.
Given that the member visits fewer than 20 times a month, find the probability that this member prefers Espresso-based drinks.
State, with a reason, whether or not the event 'prefers Espresso-based drinks' is independent of the event 'visits fewer than 10 times a month'.
