From the following list of hypothetical situations, identify those that are inde

Question

From the following list of hypothetical situations, identify those that are independent events using the given probabilities of each event and the formal definition of independence. In a yearly weather survey of a city, 32% of the days had precipitation, 25% of the days were weekend days, and 8% of the days had precipitation and were weekend days. In a television viewer survey, 30% of people watched over 3 hours of television per day, 20% of people were overweight, and 6% of people watched over 3 hours of television per day and were overweight. In a yearly study of an animal shelter, 54% of the animals were adopted, 52% of the animals were dogs, and 33% of the animals were adopted and were dogs. In a voter study. 25% of the voters had a low income, 45% of the voters were registered Democrats, and 15% of voters had a low income and were registered Democrats.

Explanation / Answer

Q-1

P(precipitation)=0.32

P(weekend)=0.25

P(precipitation and weekend)=0.08

P(precipitation) *P(weekend)=0.32*0.25=0.08= P(precipitation and weekend)

Hence, events are independent.

Q-2

P(watched >3 hrs)=0.30

P(overweight)=0.20

P(watched<3 hours and overwight)=0.06

P(Watched >3 hr )*P(overweight)=0.30*0.20=0.06= P(watched<3 hours and overwight)

So events are independent.

Q-3

P(adopted)=0.54

P(dogs)=0.52

P(adopted and dogs)=0.33

P(adopted)*P(dogs)=0.54*0.52=0.2808 P(adopted and dogs)

So events are not independent

Q-4

P(low income)=0.25

P(democrats)=0.45

P(low income and democrats)=0.15

P(low income)*P(democrats)=0.25*0.45=0.1125P(low income and democrats)

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