Tag: events and its algebra

Questions Related to events and its algebra

The probability of obtaining an even prime number on each die, when a pair of dice is rolled is

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

  1. $0$

  2. $\displaystyle\frac { 1 }{ 3 } $

  3. $\displaystyle\frac { 1 }{ 12 } $

  4. $\displaystyle\frac { 1 }{ 36 } $

Show answer
Correct Option: D
Explanation:

When two dice are rolled, the number of outcomes is $36$.
The only even prime number is $2$.
Let $E$ be the event of getting an even prime number on each die.
$\therefore E=\left{ \left( 2,2 \right)  \right} $
$\Rightarrow P\left( E \right) =\displaystyle\frac { 1 }{ 36 } $
Therefore, the correct answer is (D).

If the letters of the word  $"ATTEMPT"$  are written down at random. The probability that all the  $T's$  come together is

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

  1. $1/21$

  2. $6/7$

  3. $1/7$

  4. $1/42$

Show answer
Correct Option: C
Explanation:

Number of ways of arranging the words keeping all $T's$ together is  $5!$

Number of ways of arranging the words  is  $\dfrac{7!}{3!}$
Probability that all the $T's$  together is $\dfrac{5! }{\dfrac{7!}{3!}}=\dfrac{1}{7}$

The probability of getting number 10 in a throw of a dice is ____.

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

  1. 0

  2. 1

  3. 0.5

  4. 0.75

Show answer
Correct Option: A
Explanation:

Since the outcome of a throw of dice can never be 10, the probability is 0.

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

Show answer
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.