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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.