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Stats 3.2 Conditional Probability With Contingency Tables HOMEWORK Find each probability or conditional probability using the tables below. *Remember that P(B|A) means that event A occurred first, and that is the category you look at; it will be the denominator of your fraction. Then find the number of times event B occurred out of event A; that will be your numerator. I have done a few for you. The table below shows the gender of a sample of 100 animals at a shelter. 52 are male, 48 are female (rows across). 51 animals are dogs, while 49 are cats (columns going down). Use this table to answer questions 1 – 6. 1. Find the probability that an animal is a dog. Written as P(dog). This is NOT a conditional probability—it does not use the phrase “given that”. This implies the # of dogs in the sample out of ALL objects in the sample. So P(dog) = 51 . 100 2. Find the probability that an animal is a cat, given that it is a male. Written as P(cat|male). This IS a conditional probability, as we are going to look at all MALE animals first, then out of the males, find the # that are cats. There are 52 male animals, which will be our denominator. Out of the male animals, there are 10 that are cats. So, P(cat|male) = 10 52 3. Find the probability that an animal is a male, given that it is a cat. Written as P(male|cat). Again, this is another conditional probability. We are going to look at CAT first, which will be our denominator. Out of the cats, find the # of MALES; this will be our numerator. So P(male|cat) = 10 . Notice that this fraction is not the same as the fraction in #2. Switching the 49 order of the events changes the outcome. The numerator is the same because there are always 10 cats that are male. You will often find that P(B|A) P(A|B) 4. Find the probability that an animal is female. 5. Find the probability that an animal is a female, given that it is a dog. 6. Find P(dog|male) Use the contingency table below to answer questions 7 – 11. 7. Find the probability that someone did not take medicine. 8. Find the probability that a cold lasted 1 – 3 days. 9. Find the probability that a cold lasted 1 -3 days, given that a person took medicine. 10. Find P(4-7 days) 11. Find P(medicine not taken|4-7 days) Use the contingency table below to answer questions 12-16. 12. Find the probability that a person did not get a GI illness. 13. Find the probability that a person got a GI illness, given that they ate a burrito. 14. Find the probability a person ate burritos. 15. Find P(did not eat burritos|did not get Gil illness) 16. Find P(Got GI illness) and compare it to P(Got GI illness|ate burritos). Are they the same? What do you think this means in terms of stomach issues and eating burritos.