# Mathematics Questions and Answers – Probability – Events-1

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This set of Mathematics Multiple Choice Questions & Answers (MCQs) focuses on “Probability – Events-1”.

1. Set which contains all possible outcomes is __________________
a) event
b) empty set
c) sample space
d) probability

Explanation: Set which contains all possible outcomes is called sample space. It can also be called universal set.

2. Any subset of sample space is known as _____________
a) event
b) empty set
c) sample space
d) probability

Explanation: Any subset of sample space is known as event. Event means occurrence of some particular outcomes.

3. Which symbol denote impossible event?
a) S
b) Φ
c) β
d) μ

Explanation: Impossible event has no outcome in favour. So, it is denoted by empty set Φ.

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

Explanation: Impossible event has no outcome in favour. And probability is ratio of number of outcomes in favour to the total number of possible outcomes. So, probability of impossible event is zero.

5. Which symbol denotes sure event?
a) S
b) Φ
c) β
d) μ

Explanation: Sure event has all outcomes in favour.
So, it is denoted by sample space S.

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

Explanation: Sure event has all outcomes in favour i.e. number of outcomes in favour equal to the total number of possible outcomes.
And probability is ratio of number of outcomes in favour to the total number of possible outcomes.
So, probability of sure event will be 1.

7. Which of the following cannot be the value of probability?
a) 1
b) -1
c) 0
d) 1/2

Explanation: Since probability is ratio of number of outcomes in favour to the total number of possible outcomes. So, it cannot be negative.

8. Which of the following cannot be the value of probability?
a) 1
b) 1/4
c) 0
d) 2

Explanation: Since probability is ratio of number of outcomes in favour to the total number of possible outcomes. And number of outcomes in favour are always less than or equal to total number of possible outcomes. So, probability is always less than or equal to 1.

9. What is the probability of getting a number greater than 6 on dice?
a) 0
b) 1/2
c) 1/3
d) 1

Explanation: Since number greater than 6 cannot appear on dice so probability of getting a number greater than 6 is zero.

10. If an event has only one sample point then it is called _________________
a) simple event
b) compound event
c) impossible event
d) sure event

Explanation: If an event has only one sample point then it is called simple event.
e.g. All heads on tossing n coins.

11. If an event has more than one sample point then it is called _____________
a) simple event
b) compound event
c) impossible event
d) sure event

Explanation: If an event has more than one sample point then it is called compound event.
e.g. at least one head appears on tossing n coins.

12. If two coins are tossed simultaneously then “Exactly one head appears” is simple event or not.
a) True
b) False

Explanation: If two coins are tossed simultaneously then S = {HH, HT, TH, TT}.
“Exactly one head appears” includes HT, TH. It has more than one sample point so it is compound event not simple event.

13. For every event there exist some complementary event.
a) True
b) False

Explanation: Yes, for every event there exist some complementary event. If the event is A then complementary event is not A.

14. What is a complementary event for “At least one head appears” if two coins are tossed simultaneously?
b) At least one tail appears
c) At most one tail appears

Explanation: We know complementary of at least one is none. So, complementary event for “At least one head appears” is none head appears.

15. What is the representation of complementary event of event A?
a) S-A
b) A-S
c) S
d) S+A 