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Welcome to the Discrete Probability MCQs Page

Dive deep into the fascinating world of Discrete Probability with our comprehensive set of Multiple-Choice Questions (MCQs). This page is dedicated to exploring the fundamental concepts and intricacies of Discrete Probability, a crucial aspect of Discrete Mathematics. In this section, you will encounter a diverse range of MCQs that cover various aspects of Discrete Probability, from the basic principles to advanced topics. Each question is thoughtfully crafted to challenge your knowledge and deepen your understanding of this critical subcategory within Discrete Mathematics.

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Check out the MCQs below to embark on an enriching journey through Discrete Probability. Test your knowledge, expand your horizons, and solidify your grasp on this vital area of Discrete Mathematics.

Note: Each MCQ comes with multiple answer choices. Select the most appropriate option and test your understanding of Discrete Probability. You can click on an option to test your knowledge before viewing the solution for a MCQ. Happy learning!

Discrete Probability MCQs | Page 7 of 10

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Q61.
Suppose a fair eight-sided die is rolled once. If the value on the die is 1, 3, 5 or 7 the die is rolled a second time. Determine the probability that the sum of values that turn up is at least 8?

a.

\(\frac{32}{87}\)

b.

\(\frac{12}{43}\)

c.

\(\frac{6}{13}\)

d.

\(\frac{23}{64}\)

Discuss
Answer: (d).\(\frac{23}{64}\)
Q62.
A jar containing 8 marbles of which 4 red and 4 blue marbles are there. Find the probability of getting a red given the first one was red too.

a.

\(\frac{4}{13}\)

b.

\(\frac{2}{11}\)

c.

\(\frac{3}{7}\)

d.

\(\frac{8}{15}\)

Discuss
Answer: (c).\(\frac{3}{7}\)
Q63.
A bin contains 4 red and 6 blue balls and three balls are drawn at random. Find the probability such that both are of the same color.

a.

\(\frac{10}{28}\)

b.

\(\frac{1}{5}\)

c.

\(\frac{1}{10}\)

d.

\(\frac{4}{7}\)

Discuss
Answer: (b).\(\frac{1}{5}\)
Q64.
A bucket contains 6 blue, 8 red and 9 black pens. If six pens are drawn one by one without replacement, find the probability of getting all black pens?

a.

\(\frac{8}{213}\)

b.

\(\frac{8}{4807}\)

c.

\(\frac{5}{1204}\)

d.

\(\frac{7}{4328}\)

Discuss
Answer: (b).\(\frac{8}{4807}\)
Q65.
What is the sequence depicted by the generating series 4 + 15x² + 10x³ + 25x⁵ + 16x⁶+⋯?

a.

10, 4, 0, 16, 25, …

b.

0, 4, 15, 10, 16, 25,…

c.

4, 0, 15, 10, 25, 16,…

d.

4, 10, 15, 25,…

Discuss
Answer: (c).4, 0, 15, 10, 25, 16,…
Q66.
What is the generating function for the sequence 1, 6, 16, 216,….?

a.

\(\frac{(1+6x)}{x^3}\)

b.

\(\frac{1}{(1-6x)}\)

c.

\(\frac{1}{(1-4x)}\)

d.

1-6x²

Discuss
Answer: (b).\(\frac{1}{(1-6x)}\)
Q67.
What is the generating function for generating series 1, 2, 3, 4, 5,… ?

a.

\(\frac{2}{(1-3x)}\)

b.

\(\frac{1}{(1+x)}\)

c.

\(\frac{1}{(1−x)^2}\)

d.

\(\frac{1}{(1-x2)}\)

Discuss
Answer: (c).\(\frac{1}{(1−x)^2}\)
Q68.
What is the generating function for the generating sequence A = 1, 9, 25, 49,…?

a.

1+(A-x²)

b.

(1-A)-1/x

c.

(1-A)+1/x²

d.

(A-x)/x³

Discuss
Answer: (b).(1-A)-1/x
Q69.
What is the recurrence relation for the sequence 1, 3, 7, 15, 31, 63,…?

a.

aₙ = 3aₙ₋₁−2aₙ₊₂

b.

aₙ = 3aₙ₋₁−2aₙ₋₂

c.

aₙ = 3aₙ₋₁−2aₙ₋₁

d.

aₙ = 3aₙ₋₁−2aₙ₋₃

Discuss
Answer: (b).aₙ = 3aₙ₋₁−2aₙ₋₂
Q70.
What is multiplication of the sequence 1, 2, 3, 4,… by the sequence 1, 3, 5, 7, 11,….?

a.

1, 5, 14, 30,…

b.

2, 8, 16, 35,…

c.

1, 4, 7, 9, 13,…

d.

4, 8, 9, 14, 28,…

Discuss
Answer: (a).1, 5, 14, 30,…
Page 7 of 10

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