Problem #1 is at the end of these notes.
A pair of fair six-sided dice is rolled. What is the probability that
a. The sum of the uppermost numbers is less than or equal to 6?
b. At least one 1 is cast?
.
Problem #1 is at the end of these notes.
An experiment consists of drawing a card, then another, at random, from a well-shuffled standard deck
of 52 playing cards.
Find the probability that:
a. the second card drawn is a queen.
b. the first card was a queen given that the second card is a queen.
Problem #1 is at the end of these notes.
Problem #1 is at the end of these notes.
(From Durbin et.al. "Biological Sequence Analysis", Cambridge University Press, 1998) A rare genetic
disease is
discovered. Although only one in a million people carry it, you consider getting screened. You are told
that the genetic test is
extremely good; it is 100% sensitive (it is always correct if you have the disease) and 99.99% specific (it
gives a false positive
result only 0.01% of the time). Having recently learned Bayes' theorem, you decide not to take the test.
Why?
Problem #1 is at the end of these notes.
A survey conducted by an independent agency for the National Lung Society found that of 2000 women,
680 were heavy
smokers and 50 had emphysema. Of those who had emphysema, 42 were also heavy smokers. Using the
data in this survey,
determine whether the events “being a heavy smoker” and “having emphysema” are independent
events.
Problem #1 is at the end of these notes.
The Acrosonic model F loudspeaker system has four loudspeaker components: a woofer, a midrange, a
tweeter, and an
electrical crossover. The quality-control manager of Acrosonic has determined that on the average 1% of
the woofers, 0.8% of
the midranges, and .5% of the tweeters are defective, while 1.5% of the electrical crossovers are
defective. Determine the
probability that a loudspeaker system selected at random coming off the assembly line and before final
inspection is not
defective. Assume that the defects in the manufacturing of the components are unrelated.
Problem #1 is at the end of these notes.
Find the probability that:
a. The person is over 25 and purchases 3 or more jeans annually.
b. The person is older than 18 or purchases 1 pair of jeans
annually.
c. The person is in the age group 12-18 and purchases at most 2
pairs of jeans annually
Problem #1 is at the end of these notes.
On the basis of data obtained from the National Institute of dental Research, it has been determined
that 42% of 12-year-olds
have never had a cavity, 34% of 13-year-olds have never had a cavity, and 28% of 14-year-olds have
never had a cavity.
Suppose a child is selected at random from a group of 24 junior high school students that includes six
12-year-olds, eight 13year-olds, and ten 14-year-olds. If this child does not have a cavity, what is the probability that this child
is 14 years old?
Problem #1 is at the end of these notes.
Urn A contains 2 white and 4 red balls. Urn B contains 1 white and 1 red ball. A ball is first drawn
from urn A, and then put in
urn B. A second ball is then drawn from urn B.
a. What is the probability that the ball drawn from urn B is white?
b. What is the (conditional) probability that the transferred ball was white given that a white ball is
drawn from urn B?