MA2224 Worksheet 2
(1) Let X represent the number on the top of a fair 6-sided die. Let Y = 10 − 2X.
(a) Find the mean and variance of X.
(b) Find the mean and variance of Y .
(2) Suppose that the probability that someone in NYC has been exposed to Covid19 is 90%.
(a) Find the probability that at most 18 out of 20 randomly chosen people
in NYC have been exposed to Covid-19.
(b) Find the probability that the 5th person you survey is the first one that
was never exposed to Covid-19.
(c) Find the probability that 20 people must be tested in order to find the
15th person who has been exposed to Covid-19.
(d) Find the probability that at most 3 people will be found who never tested
positive before they find the 15th person who has been exposed to Covid19.
(3) (a) In a classroom of 30 students, 10 are math majors and 20 are CS majors.
Randomly select 7 students, what is the probability that there are at least
5 CS majors selected?
(b) In a classroom of 30 students, 10 are math majors and 20 are CS majors.
They are randomly called out to answer some questions. Assume that no
one will be called more than once, what is the probability that the 5th
student called out is the 3rd CS major being called?
(4) Let X be the random variable counting the number of times the number 1
appears when rolling six fair four-sided die.
(a) Find P (X ≥ 3).
(b) Find the cumulative distribution function of X.
(c) Find the mean and standard deviation of X.
(d) Define Y = 5X − 4, find the mean and standard deviation of Y .
(5) The probability that you find an Instagram story interesting is 5%.
(a) If you watch 20 Instagram stories, what is the probability you find more
than 3 interesting?
(b) What is the probability that the 15th story you watch is the second
interesting one?
(c) How many stories can you expect to watch before you see one interesting?
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(d) What is the probability that you have to watch more than 15 stories
before you see an interesting one.
(e) To control your addiction to your phone, you only watch 10 stories at a
time and then take a break. If you do this 15 times a day, what is the
probability that you will see at least 2 interesting stories in at least 5 of
these sessions?
(6) The East Coast suffered seven major hurricanes in 2021. Assume that this is
the average number of hurricanes each year and that the occurrence of hurricanes follows a Poisson distribution. Find the probability that in the next
two years the east coast will be hit by a number of hurricanes between 15 and
18 (inclusive).
(7) A certain type of aluminum screen has, on average, one flaw in a 100-foot roll.
Assume that the flaw distribution approximately follows the Poisson distribution.
(a) Find the probability that a 100-foot roll has at most 2 flaws.
(b) Suppose that I bought 10 200-foot rolls, find the probability that there
are exactly 3 rolls that have no flaws in them.
(c) Suppose that a store had many 200-foot rolls in storage, a clerk is doing
inspections. What is the probability that the 15th roll he inspected was
the 3rd one that has no flaws in it?