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Sample Questions

 

Introduction to Probability

 

Counting Techniques

 

Scenario I
An experiment consists of rolling a six-sided die, numbered 1 through 6, once, and flipping a two-sided coin, labelled heads and tails, once. An outcome is the letter/number pair formed by the head or tail of the upper side of the coin and the number that shows on the upper most face of the die. The die and the coin are fair, meaning that each face has the same probability of showing upper most on any roll or flip.

1) What elements are contained in the universe for this experiment?

 a)  U = {1, 2, 3, 4, 5, 6}.
 b)  U = {H, T}.
 c)  U = {H1, H2, H3, H4, H5, H6, T1, T2, T3, T4, T5, T6}.
 d)  U = {H, T, 1, 2, 3, 4, 5, 6}.
 e)  None of the above.



2) What is the point probability for element e6 = {H6}?

 a)  P({H6}) = 0.083.
 b)  P({T6}) = 0.083.
 c)  P({H6}) = 0.830.
 d)  P({H6}) = 0.038.
 e)  None of the above.



3) What elements are contained in A if event A is defined as a die value greater than or equal to 5?

 a)  A = {5, 6}.
 b)  A = {H5, H6}.
 c)  A = {H6, T6}.
 d)  A = {H5, H6, T5, T6}.
 e)  None of the above.



4) What is the probability of A if event A is defined as a die value greater than or equal to 5?

 a)  P(A) = 0.166.
 b)  P(A) = 0.25.
 c)  P(A) = 0.333.
 d)  P(A) = 0.30.
 e)  None of the above.



5) What elements are contained in B if event B is defined as an odd die value and a tail coin value?

 a)  A = {T1, T3, T5}.
 b)  B = {T1, T3, T5}.
 c)  B = {H1, H3, H5}.
 d)  B = {T2, T4, T6}.
 e)  None of the above.



6) What is the probability of B if event B is defined as an odd die value and a tail coin value?

 a)  P(B) = 0.50.
 b)  P(B) = 0.333.
 c)  P(B) = 0.20.
 d)  P(B) = 0.25.
 e)  None of the above.



7) What elements are contained in C if event C is defined as a die value less than 4 and a head coin value?

 a)  C = {H1, H2, H3}.
 b)  C = {H1, H2, H3, H4}.
 c)  D = {H1, H2, H3}.
 d)  C = {T1, T2, T3}.
 e)  None of the above.



8) What is the probability of C if event C is defined as a die value less than 4 and a head coin value?

 a)  P(C) = 0.40.
 b)  P(C) = 0.25.
 c)  P(C) = 0.333.
 d)  P(A) = 0.25.
 e)  None of the above.





Scenario II
A retail chain store warehouse has a steady stream of deliveries from suppliers and shipments to stores. The warehouse manager is expecting 6 deliveries in the next 3 hours from suppliers A through F.

9) How many ways are there for three of these deliveries to arrive at the warehouse in first, second, and third order?

 a)  18.
 b)  360.
 c)  120.
 d)  60.
 e)  None of the above.



10) For logistical reasons, the manager needs for the delivery from supplier D to arrive first, that from supplier F to arrive second, and that from supplier B to arrive third. What is the probability of this event occurring?

 a)  16.67%.
 b)  0.83%.
 c)  4.17%.
 d)  8.33%.
 e)  None of the above.



11) The manager finds that she also needs the delivery from supplier A to arrive fourth. How many ways are there for four of these deliveries to arrive at the warehouse in first, second, third, and fourth order?

 a)  720.
 b)  240.
 c)  120.
 d)  360.
 e)  None of the above.



12) What is the probability of the event in 11) occurring?

 a)  0.14%.
 b)  0.56%.
 c)  2.78%.
 d)  0.28%.
 e)  None of the above.



13) The delivery fom supplier D arrives first. How many ways are there for five remaining deliveries to arrive at the warehouse in second, third, and fourth order?

 a)  60.
 b)  20.
 c)  120.
 d)  80.
 e)  None of the above.



14) What is the probability of the event in 13) occurring?

 a)  0.17%.
 b)  0.33%.
 c)  1.67%.
 d)  3.33%.
 e)  None of the above.





Scenario III
An income tax preparation firm hires many tax prepares every January. One local office needs to hire 5 tax preparers out of an applicant pool of 15.

15) In how many ways can the needed preparers be hired from the applicant pool?

 a)  303.
 b)  3,003.
 c)  5,005.
 d)  2,002.
 e)  None of the above.



16) What is the probability of the office hiring a random grouping of 5 tax preparers?

 a)  0.0333%.
 b)  0.0999%.
 c)  0.0199%.
 d)  0.0500%.
 e)  None of the above.



17) The applicant pool increases to 18. In how many ways can the needed preparers be hired from this bigger applicant pool?

 a)  12,870.
 b)  18,564.
 c)  8,568.
 d)  3,003.
 e)  None of the above.



18) What is the probability of the office hiring a random grouping of 5 tax preparers from this bigger applicant pool?

 a)  0.0078%.
 b)  0.0054%.
 c)  0.0333%.
 d)  0.0117%.
 e)  None of the above.



19) The office hires one preparer from the applicant pool in 17). In how many ways can the remaining needed tax preparers be hired from the remaining applicant pool?

 a)  6,188.
 b)  2,380.
 c)  3,060.
 d)  1,994.
 e)  None of the above.



20) What is the probability of the office hiring a random grouping of 4 tax preparers from the remaining applicant pool?

 a)  0.0162%.
 b)  0.0327%.
 c)  0.0502%.
 d)  0.0420%.
 e)  None of the above.






 

 

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