Business Smarts - Sample Module for Introduction to Probability

Scenario I
An experiment consists of rolling a decahedral die (ten-sided die). Its 10 faces are numbered 1 through 10 with one number on each face. An outcome is the number that shows on the upper most face of the die. The die is fair, meaning that each face has the same probabiity of showing upper most on any roll.

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

 a)  U = {1, 2, 3, 4, 5, 6}.

 b)  U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}.

 c)  U < {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}.

 d)  A = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}.

 e)  None of the above.

2) What is the point probability for element e₂ = {2}?

 a)  P({2}) = 0.10.

 b)  P({2}) = 0.01.

 c)  P({2}) = 1.0.

 d)  P({4}) = 0.10.

 e)  None of the above.

3) What is the point probability for element e₀ = {0}?

 a)  P({0}) = 0.10.

 b)  P({1}) = 0.10.

 c)  P({0}) = 1.0.

 d)  P({0}) = 0.05.

 e)  None of the above.

4) What elements are contained in A if event A is defined as rolling the die and obtaining a value greater than 6?

 a)  A = {1, 2, 3, 4, 5, 6}.

 b)  U = {7, 8, 9, 10}.

 c)  A = {7, 8, 9, 10}.

 d)  A = {6, 7, 8, 9, 10}.

 e)  None of the above.

5) What is the probability of A if event A is defined as rolling the die and obtaining a value greater than 6?

 a)  P(A) = 0.10.

 b)  P(A) = 0.40.

 c)  P(C) = 0.40.

 d)  P(A) = 0.60.

 e)  None of the above.

6) What elements are contained in B if event B is defined as rolling the die and obtaining a value less than 4?

 a)  B = {5, 6, 7. 8, 9, 10}.

 b)  B = {1, 2, 3, 4}.

 c)  A = {1, 2, 3}.

 d)  B = {1, 2, 3}.

 e)  None of the above.

7) What is the probability of B if event B is defined as rolling the die and obtaining a value less than 4?

 a)  P(A) = 0.30.

 b)  P(B) = 0.30.

 c)  P(B) = 0.40.

 d)  P(B) = 0.20.

 e)  None of the above.

8) What elements are contained in C if event C is defined as rolling the die and obtaining a value greater than 3 and less than 7?

 a)  C = {4, 5, 6}.

 b)  C = {4, 6, 8}.

 c)  D = {4, 5, 6}.

 d)  C = {3, 4, 5}.

 e)  None of the above.

9) What is the probability of C if event C is defined as rolling the die and obtaining a value greater than 3 and less than 7?

 a)  P(C) = 0.40.

 b)  P(B) = 0.30.

 c)  P(C) = 0.30.

 d)  P(C) = 0.20.

 e)  None of the above.

10) What elements are contained in D if event D is defined as rolling the die and obtaining an odd value less than or equal to 6?

 a)  D = {2, 4, 6}.

 b)  D = {1, 2, 3, 4, 5, 6}.

 c)  B = {1, 3, 5}.

 d)  D = {1, 3, 5}.

 e)  None of the above.

11) What is the probability of D if event D is defined as rolling the die and obtaining an odd value less than or equal to 6?

 a)  P(D) = 0.20.

 b)  P(D) = 0.30.

 c)  P(E) = 0.30.

 d)  P(D) = 0.40.

 e)  None of the above.

Scenario II
A person keeps his socks in a drawer of his dresser or bureau. He has 10 socks that are black, 6 socks that are red, and 4 socks that are green. An experiment is the selection of one sock. Each of the 20 socks have the same chance of being selected in an experiment.

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

 a)  U = {b, b, b, b, b, b, r, r, r, r, r, r, g, g, g, g}.

 b)  U = {b, b, b, b, b, b, b, b, b, b, r, r, r, r, r, r, g, g, g, g}.

 c)  Z = {b, b, b, b, b, b, b, b, b, b, r, r, r, r, r, r, g, g, g, g}.

 d)  U = {b, b, b, b, b, b, b, b, b, b, r, r, r, r, r, r}.

 e)  None of the above.

13) What is the point probability for element e₁₁ = {r}?

 a)  P({r}) = 0.10.

 b)  P({g}) = 0.05.

 c)  P({b}) = 0.05.

 d)  P({r}) = 0.05.

 e)  None of the above.

14) What elements are contained in E if event E is defined as selecting a green sock?

 a)  E = {g, g, g, g}.

 b)  E = {b, b, b, b}.

 c)  F = {g, g, g, g}.

 d)  E = {g, g, g}.

 e)  None of the above.

15) What is the probability of E if event E is defined as selecting a green sock?

 a)  P(E) = 0.20.

 b)  P(E) = 0.30.

 c)  P(E) = 0.10.

 d)  P(E) = 0.05.

 e)  None of the above.

16) What elements are contained in F if event F is defined as selecting a red sock?

 a)  F = {g, g, g, g}.

 b)  E = {r, r, r, r, r, r}.

 c)  F = {r, r, r, r, r, r}.

 d)  F = {r, r, r, r}.

 e)  None of the above.

17) What is the probability of F if event F is defined as selecting a red sock?

 a)  P(F) = 0.40.

 b)  P(F) = 0.30.

 c)  P(E) = 0.30.

 d)  P(F) = 0.20.

 e)  None of the above.

18) What elements are contained in G if event G is defined as selecting a black sock?

 a)  H = {b, b, b, b, b, b, b, b, b, b}.

 b)  G = {g, g, g, g, g, g, g, g, g, g}.

 c)  G = {b, b, b, b, b, b}.

 d)  G = {b, b, b, b, b, b, b, b, b, b}.

 e)  None of the above.

19) What is the probability of G if event G is defined as selecting a black sock?

 a)  P(G) = 0.50.

 b)  P(G) = 0.40.

 c)  P(G) = 0.60.

 d)  P(G) = 1.00.

 e)  None of the above.

20) What elements are contained in H if event H is defined as selecting a white sock?

 a)  H = {w, w, w, w, w}.

 b)  H = {w, w, w}.

 c)  H = {w, w, w, w, w, w}.

 d)  H = {w, w}.

 e)  None of the above.

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