Question

A survey asked people whether their pets are picky eaters. For these results, are being a picky eater and being a cat independent or dependent events?
Justify your answer.

Answer 1

Answer: Choice B. Dependent; probabilities are not equal

P(picky) = 34%

P(picky | cat) = 44%

This is a vertical bar separating "picky" and "cat". It is not an uppercase letter i or lowercase letter L.

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Explanation:

There are 17 total picky eaters out of 50 pets total. The probability of randomly choosing a picky eater is

P(picky) = 17/50 = 0.34 = 34%

The notation P(picky | cat) translates to "probability of getting a picky eater given the pet is a cat". In other words, we have prior knowledge the pet is a cat. So we only focus on the cat row. We have 11 picky cats out of 25 cats total. This means

P(picky | cat) = 11/25 = 0.44 = 44%

Notice how this result is different from 34% found earlier. The fact that we have prior knowledge the pet selected is a cat changes the probability of P(picky). This means the events are dependent. If they were independent events, then P(picky) = P(picky | cat) would be true.