Tag: introduction of probability theory

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Questions Related to introduction of probability theory

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

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

  1. $0$
  2. $\displaystyle\frac { 1 }{ 3 } $
  3. $\displaystyle\frac { 1 }{ 12 } $
  4. $\displaystyle\frac { 1 }{ 36 } $
Reveal answer Fill a bubble to check yourself
D Correct answer
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).

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

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

  1. $1/21$
  2. $6/7$
  3. $1/7$
  4. $1/42$
Reveal answer Fill a bubble to check yourself
C Correct answer
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 $\dfrac{5! }{\dfrac{7!}{3!}}=\dfrac{1}{7}$

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

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?

  1. $\displaystyle\frac{6}{13}$
  2. $\displaystyle\frac{3}{13}$
  3. $\displaystyle\frac{7}{13}$

  4. None
Reveal answer Fill a bubble to check yourself
C Correct answer
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)$=13- 6=7C _1$
$\therefore  probability=\dfrac{n(E)}{n(S)}=\frac{7}{13}$

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

The probability of a certain event is 

  1. $0$
  2. $1$
  3. greater than $1$
  4. less than $0$
Reveal answer Fill a bubble to check yourself
B Correct answer
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.
Multiple choice maths introduction of probability theory types of events some more terms in probability events and its algebra

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

  1. sure event

  2. impossible event

  3. equally likely event

  4. none of these
Reveal answer Fill a bubble to check yourself
B Correct answer
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.
$P(E)=\frac{0}{6}=0$