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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 6 of 10

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Q51.
A Random Variable X can take only two values, 4 and 5 such that P(4) = 0.32 and P(5) = 0.47. Determine the Variance of X.

a.

8.21

b.

12

c.

3.7

d.

4.8

Discuss
Answer: (c).3.7
Q52.
A 6-sided die is biased. Now, the numbers one to four are equally likely to happen, but five and six is thrice as likely to land face up as each of the other numbers. If X is the number shown on the uppermost face, determine the expected value of X when 6 is shown on the uppermost face.

a.

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

b.

\(\frac{3}{5}\)

c.

\(\frac{2}{7}\)

d.

\(\frac{21}{87}\)

Discuss
Answer: (a).\(\frac{13}{4}\)
Q53.
A fair cubical die is thrown twice and their scores summed up. If the sum of the scores of upper side faces by throwing two times a die is an event. Find the Expected Value of that event.

a.

48

b.

76

c.

7

d.

132

Discuss
Answer: (c).7
Q54.
A random variable X can take only two values, 2 and 4 i.e., P(2) = 0.45 and P(4) = 0.97. What is the Expected value of X?

a.

3.8

b.

2.9

c.

4.78

d.

5.32

Discuss
Answer: (c).4.78
Q55.
A single card is drawn from a standard deck of playing cards. What is the probability that the card is a face card provided that a queen is drawn from the deck of cards?

a.

\(\frac{3}{13}\)

b.

\(\frac{1}{3}\)

c.

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

d.

\(\frac{1}{52}\)

Discuss
Answer: (b).\(\frac{1}{3}\)
Q56.
Naina receives emails that consists of 18% spam of those emails. The spam filter is 93% reliable i.e., 93% of the mails it marks as spam are actually a spam and 93% of spam mails are correctly labelled as spam. If a mail marked spam by her spam filter, determine the probability that it is really spam.

a.

50%

b.

84%

c.

39%

d.

63%

Discuss
Answer: (a).50%
Q57.
A meeting has 12 employees. Given that 8 of the employees is a woman, find the probability that all the employees are women?

a.

\(\frac{11}{23}\)

b.

\(\frac{12}{35}\)

c.

\(\frac{2}{9}\)

d.

\(\frac{1}{8}\)

Discuss
Answer: (c).\(\frac{2}{9}\)
Q58.
A cupboard A has 4 red carpets and 4 blue carpets and a cupboard B has 3 red carpets and 5 blue carpets. A carpet is selected from a cupboard and the carpet is chosen from the selected cupboard such that each carpet in the cupboard is equally likely to be chosen. Cupboards A and B can be selected in \(\frac{1}{5}\) and \(\frac{3}{5}\) ways respectively. Given that a carpet selected in the above process is a blue carpet, find the probability that it came from the cupboard B.

a.

\(\frac{2}{5}\)

b.

\(\frac{15}{19}\)

c.

\(\frac{31}{73}\)

d.

\(\frac{4}{9}\)

Discuss
Answer: (b).\(\frac{15}{19}\)
Q59.
Mangoes numbered 1 through 18 are placed in a bag for delivery. Two mangoes are drawn out of the bag without replacement. Find the probability such that all the mangoes have even numbers on them?

a.

43.7%

b.

34%

c.

6.8%

d.

9.3%

Discuss
Answer: (c).6.8%
Q60.
A family has two children. Given that one of the children is a girl and that she was born on a Monday, what is the probability that both children are girls?

a.

\(\frac{13}{27}\)

b.

\(\frac{23}{54}\)

c.

\(\frac{12}{19}\)

d.

\(\frac{43}{58}\)

Discuss
Answer: (a).\(\frac{13}{27}\)
Page 6 of 10

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