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A nationwide survey conducted by the National Cancer Society revealed the following information. Of 10,000 people surveyed, 3200 were "heavy coffee drinkers" and 160 had cancer of the pancreas. Of those who had cancer of the pancreas, 132 were heavy coffee drinkers. Using the data in this survey, determine whether the events "being a heavy coffee drinker" and "having cancer of the pancreas" are independent events.

Short Answer

Expert verified
The events "being a heavy coffee drinker" and "having cancer of the pancreas" are not independent events, as the calculated probabilities P(A and B) = 132/10000 ≠ P(A) * P(B) = 512000/100000000.

Step by step solution

01

Define the probabilities of the events

First, let's define the probabilities of the events: - Event A: being a heavy coffee drinker; - Event B: having cancer of the pancreas. We can calculate the probabilities of these events using the following formulas: - P(A) = the number of heavy coffee drinkers / the total number of people surveyed; - P(B) = the number of people with cancer of the pancreas / the total number of people surveyed. Using the data from the survey, we have: - P(A) = 3200 / 10000; - P(B) = 160 / 10000.
02

Check if the events are independent

Now we can check if the events A and B are independent. To do this, we need to calculate the probability of both events occurring, P(A and B), and check if it's equal to the product of the individual probabilities, P(A) * P(B). The probability of both events occurring can be calculated as follows: - P(A and B) = number of heavy coffee drinkers with cancer of the pancreas / the total number of people surveyed = 132 / 10000. Now, let's check if P(A and B) = P(A) * P(B). - P(A and B) = 132 / 10000; - P(A) * P(B) = (3200 / 10000) * (160 / 10000) = 512000 / 100000000. To determine if the events are independent, we compare P(A and B) and P(A) * P(B): - 132 / 10000 = 512000 / 100000000. Since these probabilities are not equal, the events "being a heavy coffee drinker" and "having cancer of the pancreas" are not independent events.

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