STA220H1 Additional Problems for Probability: Events Module
1. If a woman takes an early pregnancy test, she will either test positive, meaning that the test says she
is pregnant, or test negative, meaning that the test says she is not pregnant. Suppose that if a woman
really is pregnant, there is a 98% chance that she will test positive. Also, suppose that if a woman
really is not pregnant, there is is 99% chance that she will test negative.
(a) Suppose that 1,000 women take early pregnancy tests and that 100 of them really are pregnant.
What is the probability that a randomly chosen woman from this group will test positive?
(b) Suppose that a woman from the group in (a) tests positive. What is the probability that she
really is pregnant?
2. Suppose you know that P (A) = .4 and P (B) = .1. What additional information do you need to
calculate P (A and B)?
3. The probability distribution of the number of trees that a certain disease kills every year is given in
the following table:
Number of trees killed
0 1-9 10-15 16-25 >25
0.25 0.20 0.15 0.10
(a) What is the probability that no trees are killed in a year due to the disease?
(b) What is the probability that between 1-9 or 10-15 trees are killed this year due to the disease?
4. (OpenIntro exercise 2.17) A 2010 Pew Research poll asked 1,306 Americans “From what you’ve read
and heard, is there solid evidence that the average temperature on earth has been getting warmer over
the past few decades, or not?”. The table below shows the distribution of responses by party and
ideology, where the counts have been replaced with relative frequencies.
Response
Earth is Not Don’t Know
warming warming Refuse Total
Conservative Republican 0.11 0.20 0.02 0.33
Party and Mod/Lib Republican 0.06 0.06 0.01 0.13
Ideology Mod/Cons Democrat 0.25 0.07 0.02 0.34
Liberal Democrat 0.18 0.01 0.01 0.20
Total 0.60 0.34 0.06 1.00
(a) Are believing that the earth is warming and being a liberal Democrat mutually exclusive?
(b) What is the probability that a randomly chosen respondent believes the earth is warming or is a
liberal Democrat?
(c) What is the probability that a randomly chosen respondent believes the earth is warming given
that he is a liberal Democrat?
(d) What is the probability that a randomly chosen respondent believes the earth is warming given
that he is a conservative Republican?
(e) Does it appear that whether or not a respondent believes the earth is warming is independent of
their party and ideology? Explain your reasoning.
(f) What is the probability that a randomly chosen respondent is a moderate/liberal Republican
given that he does not believe that the earth is warming?
5. If an individual is HIV negative, the EIA test has probability 0.006 of giving a positive (i.e., false
positive) result (a positive test result indicates that the individual has HIV). If 2 people are tested
who are both HIV negative then what is probability that at least one person will have a positive test
result? If 3 people are tested who are both HIV negative then what is probability that at least one
person will have a positive test result?