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.

Answer 2

The required probability of a Picky pet is 34% and for a picky cat is 44% and these events are dependent. Option B is correct.

A survey of people has shown in the image,
Events of being a picky eater and being a cat independent or dependent events to be justified.

What is probability?

Probability can be defined as a number of the desired events per unit total number of events.

Here,
Probability of  being a picky eater P(picky eater),
Total picky eater = 17, and the total number of pets is 50 (from the table in the image)
P(picky eater) = 17/50
                       = 0.340
                       =  34%
Probability for picky cat p(picky cat)
number of cats = 25 and number of picky cats = 11
P(picky cat) = 11/25
                   = 0.44
                   = 44%
The probability of both events is dependent because in the Venn diagram we can see the contributions.

Thus, The required probability of a Picky pet is 34% and for a picky cat is 44% and these events are dependent.

Learn more about probability here:

brainly.com/question/14290572

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