*Name:_________________________
SCORE:
/100
Math 3670 – Fall 2024
Quiz 1
September 12, 2024 2 pm-3:15pm
1. The exam is closed-book and closed notes. The use of a calculator is allowed
but its memory should be cleared. You are allowed to use the official formula
sheet (available on Canvas).
2. Put your name at the top of this page. Put your initials at the top of each
subsequent page. You can use extra sheets of paper if necessary.
3. Write your answers clearly, make your figures neat, and label all plots carefully.
Show your work! (No work shown and incorrect answer means no partial
credit)
4. Write your answers in the boxes AND copy them in the table below:
Penalty for not copying the answers in the table: -1/100 on your score
Score
/6
1
2a
2b
3a
3b
2c
2d
Score
/8
Score
/6
4
Score
/6
5
Score
/3
TOTAL
/29
Page 1 of 6
*Name:_________________________
Problem 1
6 points
A hand of ten cards is chosen at random without replacement from a deck of 52 cards.
What is the probability that the hand contains exactly 2 aces, 2 kings, 3 queens and 3
jacks?
Page 2 of 6
*Name:_________________________
Problem 2 TRUE/FALSE and short-answer questions
True/false questions: circle the correct answer; no partial credit.
(a) (2 points) TRUE OR FALSE?
P( A B C ) P( A) P( B) P(C )
P( B | A) P( A) P(C | A) P( A) P( B | C ) P(C )
P( A B C )
(b) (2 points) We know the following:
P( A) 0.4
P( B) 0.2
P( A B) 0.08
TRUE OR FALSE? A and B are independent events.
(c) (2 points) TRUE OR FALSE?
It is always true that 𝑃(𝐴̅|𝐵̅) = 1 − 𝑃(𝐴̅|𝐵).
(d) (2 points) TRUE OR FALSE?
Two events A and B that do not have any outcomes in common are necessarily
independent.
Page 3 of 6
*Name:_________________________
Problem 3
Four companies A, B, C, and D supply 10%, 15%, 35% and 40% of the notebooks to a
school. Past experience shows that 5%, 4%, 3%, and 2%, respectively, of the notebooks
produced by these companies are defective.
(a) 3 points If a notebook was found to be defective, what is the probability that the
notebook was supplied by A?
Answer:
(b) 3 points If a notebook was found not to be defective, what is the probability it was
not supplied by B?
Answer:
Page 4 of 6
*Name:_________________________
Problem 4
6 points
4 fair dice are tossed independently. Determine the probability that the sum of the dice
is strictly larger than 6.
Answer:
Page 5 of 6
*Name:_________________________
Problem 5
3 points
In how many ways can one scramble the letters in “ARKANSAS”?
Answer:
Page 6 of 6
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