# 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

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.

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) ∞

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

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.

4. What is the probability of a sure event?
a) 0
b) 1
c) 2
d) 3

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

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.

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

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

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.

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

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

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) = $$\frac {Number \, of \, favorable \, outcomes}{Total \, number \, of \, outcomes}$$
= $$\frac {2}{6}$$
= $$\frac {1}{3}$$

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) $$\frac {4}{9}$$

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) $$\frac {4}{9}$$

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) $$\frac {21}{26}$$

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) $$\frac {1}{26}$$

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) $$\frac {1}{26}$$

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) $$\frac {1}{52}$$

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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