Mathematics Questions and Answers – Theoretical Approach to Probability

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This set of Mathematics Multiple Choice Questions & Answers (MCQs) focuses on “Theoretical Approach to Probability”.

1. Who gave the definition of probability?
a) Euclid
b) Simon Laplace
c) Archimedes
d) Einstein
View Answer

Answer: b
Explanation: The definition of probability was given by Pierre Simon Laplace in the year 1795. Probability can be defined as the ratio of the number of favorable outcomes to the total number of possible outcomes.
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2. What is the sum of the probability of occurring an event E and the probability of not occurring the event E?
a) 0
b) -1
c) 1
d) ∞
View Answer

Answer: c
Explanation: Probability of occurring an event E = P(E)
Probability of not occurring the event E = P(E)
P(E) + P(E) = 1

3. What is the name of the event for which the probability is zero?
a) Impossible event
b) Random event
c) Exhaustive events
d) Mutual events
View Answer

Answer: a
Explanation: An event that doesn’t occur in any possible scenario is called an impossible event. The probability of an impossible event is always zero.
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4. What is the probability of a sure event?
a) 0
b) 1
c) 2
d) 3
View Answer

Answer: b
Explanation: An even that is certain to occur is called a sure event or a certain event. The probability of a sure event or a certain event is always one and it will never exceed over one.

5. What kind of an event is getting a head or a tail when a coin is tossed?
a) Impossible event
b) Equal event
c) Exhaustive event
d) Equally likely
View Answer

Answer: d
Explanation: If two or more events have an equal chance of occurrence then that kind of an event is called an equally likely event. Here, The chance of getting a head or a tail is equal so, it is an equally likely event.
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6. The probability of occurring an event is 0.45. Find the probability of not occurring the event.
a) 0.5
b) 0.45
c) 0.55
d) 0.1
View Answer

Answer: c
Explanation: The probability of occurring an event be P(E) = 0.45
The probability of not occurring the event = P(E)
P(E) + P(E) = 1
0.45 + P(E) = 1
P(E) = 0.55

7. What is the probability of selecting 8 blue balls from 10 green balls?
a) 1
b) 0
c) 0.23
d) 0.5
View Answer

Answer: b
Explanation: Selecting 8 blue balls from 10 green balls is an impossible event. An event that doesn’t occur in any possible scenario is called an impossible event. The probability of an impossible event is always zero.
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8. What is the probability of getting even numbers when a die is rolled?
a) \(\frac {1}{2}\)
b) \(\frac {3}{2}\)
c) \(\frac {1}{4}\)
d) 1
View Answer

Answer: a
Explanation: Total number of outcomes are {1, 2, 3, 4, 5, 6} = 6
Even numbers in total outcomes are {2, 4, 6} = 3
P(E) = \(\frac {Number \, of \, favorable \, outcomes}{Total \, number \, of \, outcomes}\)
= \(\frac {3}{6}\)
= \(\frac {1}{2}\)

9. What is the probability of getting factors of 3 when a die is rolled?
a) \(\frac {1}{3}\)
b) \(\frac {2}{3}\)
c) \(\frac {1}{6}\)
d) 0
View Answer

Answer: a
Explanation: Total number of outcomes are {1, 2, 3, 4, 5, 6} = 6
Factors of 3 in total outcomes are {3, 6} = 2
P(E) = \(\frac {Number \, of \, favorable \, outcomes}{Total \, number \, of \, outcomes}\)
= \(\frac {2}{6}\)
= \(\frac {1}{3}\)
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10. A bag contains 3 black, 2 brown, 4 blue balls. What is the probability of getting a brown ball?
a) \(\frac {1}{9}\)
b) \(\frac {7}{9}\)
c) \(\frac {2}{9}\)
d) \(\frac {4}{9}\)
View Answer

Answer: c
Explanation: Total number of outcomes = 3 + 2 + 4 = 9
Favorable outcomes of getting a brown ball = 2
P(E) = \(\frac {Number \, of \, favorable \, outcomes}{Total \, number \, of \, outcomes} = \frac {2}{9}\)

11. A bag contains 3 black, 7 brown, 4 green marbles. What is the probability of getting a green ball?
a) \(\frac {1}{9}\)
b) \(\frac {7}{9}\)
c) \(\frac {2}{7}\)
d) \(\frac {4}{9}\)
View Answer

Answer: c
Explanation: Total number of outcomes = 3 + 7 + 4 = 14
Favorable outcomes of getting a green ball = 4
P(E) = \(\frac {Number \, of \, favorable \, outcomes}{Total \, number \, of \, outcomes} = \frac {4}{14}\)
= \(\frac {2}{7}\)

12. What is the probability of getting a vowel in the English alphabet?
a) \(\frac {1}{21}\)
b) \(\frac {5}{19}\)
c) \(\frac {5}{26}\)
d) \(\frac {21}{26}\)
View Answer

Answer: c
Explanation: Total number of outcomes = 26
Favorable outcomes of getting a vowel = {a, e, i, o, u} = 5
P(E) = \(\frac {Number \, of \, favorable \, outcomes}{Total \, number \, of \, outcomes} = \frac {5}{26}\)

13. What is the probability of getting the letter ‘E’ in the English alphabet?
a) \(\frac {1}{21}\)
b) \(\frac {5}{19}\)
c) \(\frac {5}{26}\)
d) \(\frac {1}{26}\)
View Answer

Answer: d
Explanation: Total number of outcomes = 26
Favorable outcomes of getting ‘E’ = {E} = 1
P(E) = \(\frac {Number \, of \, favorable \, outcomes}{Total \, number \, of \, outcomes} = \frac {1}{26}\)

14. What is the probability of getting a black card from the deck of playing cards?
a) \(\frac {1}{2}\)
b) \(\frac {5}{52}\)
c) \(\frac {5}{26}\)
d) \(\frac {1}{26}\)
View Answer

Answer: a
Explanation: Total number of outcomes = 52
Favorable outcomes of getting a black card = 26
P(E) = \(\frac {Number \, of \, favorable \, outcomes}{Total \, number \, of \, outcomes} = \frac {26}{52}\)
= \(\frac {1}{2}\)

15. What is the probability of getting a card of Queen from the deck of playing cards?
a) \(\frac {1}{2}\)
b) \(\frac {1}{13}\)
c) \(\frac {5}{26}\)
d) \(\frac {1}{52}\)
View Answer

Answer: b
Explanation: Total number of outcomes = 52
Favorable outcomes of getting a card of Queen = 4
P(E) = \(\frac {Number \, of \, favorable \, outcomes}{Total \, number \, of \, outcomes} = \frac {4}{52}\)
= \(\frac {1}{13}\)

Sanfoundry Global Education & Learning Series – Mathematics – Class 10.

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Manish Bhojasia, a technology veteran with 20+ years @ Cisco & Wipro, is Founder and CTO at Sanfoundry. He is Linux Kernel Developer & SAN Architect and is passionate about competency developments in these areas. He lives in Bangalore and delivers focused training sessions to IT professionals in Linux Kernel, Linux Debugging, Linux Device Drivers, Linux Networking, Linux Storage, Advanced C Programming, SAN Storage Technologies, SCSI Internals & Storage Protocols such as iSCSI & Fiber Channel. Stay connected with him @ LinkedIn | Youtube | Instagram | Facebook | Twitter