Answer:
The probability of buying a boat trailer changes depending on whether or not a boat has been bought
Explanation:
To determine whether buying a boat and a boat trailer are independent events, we need to check if the probability of buying a boat trailer changes if we know whether or not a boat has been bought.
Let's use the formula for conditional probability to calculate the probability of buying a boat trailer given that a boat has been bought:
P(trailer | boat) = P(trailer and boat) / P(boat)
We are given that P(trailer and boat) = 44%, P(boat) = 62%, and we can calculate P(trailer) using the probability of the complement:
P(trailer) = 1 - P(no trailer) = 1 - 0.55 = 0.45
Substituting these values, we get:
P(trailer | boat) = 0.44 / 0.62 ≈ 0.71
This means that if a boat has been bought, the probability of buying a boat trailer is about 71%.
Now, we can compare this conditional probability to the marginal probability of buying a boat trailer without considering whether or not a boat has been bought. If the conditional probability is the same as the marginal probability, then buying a boat and a boat trailer are independent events.
P(trailer) = 0.45
Since P(trailer | boat) ≠ P(trailer), we can conclude that buying a boat and a boat trailer are dependent events. The probability of buying a boat trailer changes depending on whether or not a boat has been bought.