Questions:
1) Are the pairs of events described below disjoint or not, and independent or not? For
each pair, circle disjoint or not disjoint, and independent or dependent (6 points).
a) A = {you had pizza for dinner}
B = {cheese was part of that dinner}
i) Disjoint or Not Disjoint
ii) Independent or Dependent
b) A = {your pizza was delivered by a person riding a bicycle}
B = {your pizza was delivered by a person driving a car}
i) Disjoint or Not Disjoint
ii) Independent or Dependent
c) A = {your pizza had your favorite topping on it}
B = {your pizza box had words printed on it}
i) Disjoint or Not Disjoint
ii) Independent or Dependent
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2) You toss a fair coin four times. Assuming the coin tosses are independent:
a. What is the probability of getting tails four times, TTTT (4 points)?
b. What is the probability of getting exactly three heads (4 points)?
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3) A pool contractor noticed that 70% of his customers requested some sort of work on a
pool, while 40% requested some sort of work on a pool deck. Let us consider that
requests for work on pools and requests for work on decks are independent of each
other. (FYI, pool contractors do other things besides work on pools and decks.)
Using the information above, answer the following:
a) What is the probability that a randomly selected customer requested work on both a
pool and a deck (3 points)?
b) What is the probability that a randomly selected customer requested work on neither
a pool nor a deck (3 points)?
c) What is the probability that a randomly selected customer requested work on a pool
but not a deck (3 points)?
d) What is the probability that a randomly selected customer requested work on a deck
but not a pool (3 points)?
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e) Use the Venn diagram below to match the four probabilities with the four areas of
the Venn Diagram (A, B, C, D) (4 points).
Note: S refers to the entire sample space.
i) – The probability that a randomly selected customer requested
work on both a pool and a deck.
ii) – The probability that a randomly selected customer requested
work on neither a pool nor a deck.
iii) – The probability that a randomly selected customer requested
work on a pool but not a deck.
iv) – The probability that a randomly selected customer requested
work on a deck but not a pool.
S
A B C
D
Pool Deck
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4) A survey of students in the foreign language department was conducted to investigate
how many students were taking courses for the three main languages—French, Spanish,
and German. The survey sample consisted of 220 students. Only 4 of the students were
studying all three languages.
Not including the students who studied all three languages, 22 students were studying
French and Spanish, 15 students were studying Spanish and German, and 10 students
were studying German and French. Overall, 30% of the students studied French, 40%
studied Spanish, and 25% studied German.
Using the information above, complete the diagram below and answer the questions that
follow (21 points).
Note: S refers to the entire sample space. There are nine values that need to be written in
the diagram.
S =
French Spanish
German D =
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a) What is the probability of picking a student that studies French and German (4
points)?
b) What is the probability of picking a student that studies German or Spanish (4
points)?
c) If you randomly selected a student that studies German, what’s the probability they
were also studying Spanish (4 points)?
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5) Classify the following random variables as discrete or continuous (10 points).
a. V = the age of toddlers at a daycare center in months
b. Y = the total surface area of a randomly selected person’s body
c. W = the quantity of oil in a randomly selected oil spill in the sea
d. X = the quantity of pots in a randomly selected restaurant kitchen
e. Z = the total cent value of all the coins in a randomly selected person’s pocke
