MATH2030-Weekly Practice Questions(C)
Question 1
In a certain population, 10% of the people can be classified as being high risk for a
heart attack. Three people are randomly selected from this population. What is
the probability that exactly one of the three are high risk? 0.243
Question 2
Suppose we have additional information for the previous question. We know that
only 49% of the population are female. Also, of the female patients, 8% are high
risk for hearth attacked. A single person is selected at random. What is the
probability that it is a high-risk female? 0 .0392
Question 3
From a previous question, we know that 49% of the population are female. Of the
female patients, 8% are high risk for heart attack, while 12% of the male patients
are high risk. A single person is selected at random and found to be high risk.
What is the probability that it is a male? 0.6096
Question 4
A pair of fair dice is rolled. What is the probability that the second die lands on
higher value than does the first? 0.4167
Question 5.
Warren, a financial analyst has determined that there is an 8% probability that a
mutual fund will outperform the market over a year period provided that it
outperformed the market the previous year. If only 3% of mutual funds outperform
the market during any year, what is the probability that mutual fund will
outperform the market 2 years in a row? 0.0024
Question 6.
Suppose that customers of York Restaurant were asked whether they preferred
water or whether they preferred bubble tea. 70% said that they preferred water.
60% of the customers were male. 80% of the males preferred water.
a. What is the probability that a randomly selected customer is a female who
prefers bubble tea?
b. Suppose a randomly selected customer is a female, what is the probability that
the customer prefers water is __________. 0.55
0.18 , 0.55
Question 7.
Suppose a test using AI technology for diagnosing a certain serious disease is
successful in detecting the serious disease in 99.7% of all person infected but that
is incorrectly diagnoses 0.5% of all healthy people as having the serious disease.
Suppose also that it incorrectly diagnoses 1.8% of all people having another minor
disease as having the serious disease. It is known that 2% of the population have
the serious disease, 93% of the population are healthy, and 5% have the minor
disease. Given the test is positive, what is the probability that selected has the
serious disease?
Use H to represent healthy, M to represent having minor disease, and D to
represent having serious disease. 0.7823
Question 8.
A security system is manufactured with a “fail-safe” provision so that it functions
properly if any two or more of its three main components, X, Y and Z, are
functioning properly. The probabilities that components X, Y, and Z are functioning
properly are 0.98, 0.88 and 0.78, respectively. What is the probability that the
system functions properly? 0.9679
Question 9.
A recent report revealed that only 89% of active Gmail accounts use two-factor
authentication(2FA). Suppose 4 active Gmail accounts are selected at random,
compute the probability that at least 1 active Gmail account does not use 2FA.
0.3726
Question 10.
In an organic vegie packaging plant Machine A account for 60% of the plant's
output, while Machine B accounts for 40% of the plant's output. In total, 4% of the
packages are improperly sealed. Also, 3% of the packages are from Machine A and
are improperly sealed.
a. If a package selected at random is improperly sealed, what is the probability
that it came from machine A? 0.75
b. If a package selected at random came from Machine A, what is the probability
that it is improperly sealed? 0.05
c. If a package selected at random came from Machine B, what is the probability
that it is properly sealed? 0.975
