Tag: maths

Questions Related to maths

The probability of _____ event is 0.

maths introduction of probability theory types of events some more terms in probability events and its algebra

  1. Sure

  2. Impossible

  3. Exclusive

  4. None of these

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Correct Option: B
Explanation:

The probability of an impossible event is 0.

The probability of ____ event is 1.

maths introduction of probability theory types of events some more terms in probability events and its algebra

  1. Sure

  2. Impossible

  3. exclusive

  4. mutually exclusive

Show answer
Correct Option: A
Explanation:

The probability of a sure event is 1.

A bag contains $4$ red balls, $6$ blue balls and $3$ black balls. A ball is draw at random from the bag. What is the probability that the ball drawn is not blue?

maths introduction of probability theory types of events some more terms in probability events and its algebra

  1. $\displaystyle\frac{6}{13}$

  2. $\displaystyle\frac{3}{13}$

  3. $\displaystyle\frac{7}{13}$

  4. None

Show answer
Correct Option: C
Explanation:

Total no. of balls$=4+6+3=13$

Total no. of ways one ball out of 7,n(S)$=13C _1$
No.of ways of drawing 1 ball,none of then is blue,n(E)$=13- 6=7C _1$
$\therefore  probability=\dfrac{n(E)}{n(S)}=\frac{7}{13}$

The probability of a certain event is 

maths introduction of probability theory types of events some more terms in probability events and its algebra

  1. $0$

  2. $1$

  3. greater than $1$

  4. less than $0$

Show answer
Correct Option: B
Explanation:
An event which always happens is called a sure event or a certain event. So the probability of a certain event is $1$. 
For example, when we throw a die, then the event "getting a number less than $7$" is a certain event.

If P(E) = 0 then E is a/an

maths introduction of probability theory types of events some more terms in probability events and its algebra

  1. sure event

  2. impossible event

  3. equally likely event

  4. none of these

Show answer
Correct Option: B
Explanation:

$P(E)=\frac{number  of   outcomes  favorable}{Total   numbers  of  possible  outcomes}$

If P(E)=0 then the event is called impossible event.
For example -
When a dice is thrown the possible outcomes are 1,2,3,4,5 and 6.
then  the probability is to getting the number 7  in a single throw of a dice is 0 then this is called impossible event.
$P(E)=\frac{0}{6}=0$    

The probability of an impossible event is 

maths introduction of probability theory types of events some more terms in probability events and its algebra

  1. $1$

  2. $0$

  3. less than $0$

  4. greater than $1$

Show answer
Correct Option: B
Explanation:

An event that has no chance of occurring is called an impossible event. 

So, the probability of an impossible event is always zero.

The event which cannot happen is called 

maths introduction of probability theory types of events some more terms in probability events and its algebra

  1. outcome

  2. impossible event

  3. frequency

  4. none of these

Show answer
Correct Option: B
Explanation:

Event which cannot happen is called impossible event.

Any subset of sample space is called

maths introduction of probability theory types of events some more terms in probability events and its algebra

  1. event

  2. probability

  3. outcome

  4. exprement

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Correct Option: A
Explanation:

The set of all the possible outcomes is called the sample space of the experiment and is usually denoted by S. Any subset E of the sample space S is called an event. Here are some examples. Example 1 Tossing a coin

Which one of the following is an impossible event?

maths introduction of probability theory types of events some more terms in probability events and its algebra

  1. Rolling a die to get $4$

  2. Tossing a coin to get tail

  3. Choosing $4$ face cards of spades.

  4. Rolling a die for $7$.

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Correct Option: C,D
Explanation:

Choosing $4$ face cards in spades as well as rolling a die for $7$ are both impossible events.
The number of face cards in spades $= 3$ (king, queen, jack)

Rolling a die gives outcomes as $= {1, 2, 3, 4, 5, 6}$.

Choosing a queen from a deck of cards is an example of

maths introduction of probability theory types of events some more terms in probability events and its algebra

  1. compound event

  2. complementary event

  3. simple event

  4. impossible event

Show answer
Correct Option: A
Explanation:

Choosing a queen from a deck of cards is an example of compound event.
Because the total number of card $= 52$
Choosing a queen card $= 4$ (spade, diamond, heart, club)
So, more than one element of the sample space in the set representing an event, then this event is called a compound event.