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The probability that you buy a boat trailer is 55% The probability of buying a boat trailer

and a boat is 44%. If the probability of buying a boat is 62%, are buying a boat and boat
trailer independent?

User Murb
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1 Answer

6 votes

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.

User Dan Billings
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