Answer
424.8k+ views
Hint: Probability means possibility. It is a branch of mathematics that deals with the occurrence of events. It is used to predict how likely events are to happen. To find the probability of a single event to occur, first, we should know the total number of possible outcomes. Probability can range in from 0 to 1, where 0 means the event to be an impossible one and 1 indicates a certain event.
Random experiment is an experiment where we know the set of all possible outcomes but find it impossible to predict one at any particular execution. Sample space is defined as the set of all possible outcomes of a random experiment. The probability of all the events in a sample space adds up to 1.
Event is a subset of the sample space i.e. a set of outcomes of the random experiment.
\[{\text{Probability of an event}} = \dfrac{{{\text{Number of occurence of event A in S}}}}{{{\text{Total number of cases in S}}}}{\text{ }}\]
\[ = \dfrac{{n\left( A \right)}}{{n\left( S \right)}}\]
Complete step by step solution: According to the question, the tickets are drawn with replacement; the same ticket may be repeated.
Since the largest ticket is k, the tickets are chosen from 1 to K
Therefore, total number of ways of doing it = ${K^n}$
However, K may or may not have been drawn
Number of ways of choosing numbers from 1 to (K-1) = ${\left( {K - 1} \right)^n}$
Thus, number of ways in which the maximum number drawn is K = $n(A) = {K^n} - {\left( {K - 1} \right)^n}$
And total number of ways = $n(S) = {N^n}$
Therefore, Probability = $\dfrac{{n(A)}}{{n(S)}}$
Probability = $\dfrac{{{K^n} - {{\left( {K - 1} \right)}^n}}}{{{N^n}}}$
∴Option (D) is correct
Note: There are some main rules associated with basic probability:
1. P(not A)=1-P(A)
2. P(A or B)=P(event A occurs or event B occurs or both occur)
3. P(A and B)=P(both event A and event B occurs)
4. The general Addition Rule: P(A or B) = P(A) + P(B) – P(A and B)
Random experiment is an experiment where we know the set of all possible outcomes but find it impossible to predict one at any particular execution. Sample space is defined as the set of all possible outcomes of a random experiment. The probability of all the events in a sample space adds up to 1.
Event is a subset of the sample space i.e. a set of outcomes of the random experiment.
\[{\text{Probability of an event}} = \dfrac{{{\text{Number of occurence of event A in S}}}}{{{\text{Total number of cases in S}}}}{\text{ }}\]
\[ = \dfrac{{n\left( A \right)}}{{n\left( S \right)}}\]
Complete step by step solution: According to the question, the tickets are drawn with replacement; the same ticket may be repeated.
Since the largest ticket is k, the tickets are chosen from 1 to K
Therefore, total number of ways of doing it = ${K^n}$
However, K may or may not have been drawn
Number of ways of choosing numbers from 1 to (K-1) = ${\left( {K - 1} \right)^n}$
Thus, number of ways in which the maximum number drawn is K = $n(A) = {K^n} - {\left( {K - 1} \right)^n}$
And total number of ways = $n(S) = {N^n}$
Therefore, Probability = $\dfrac{{n(A)}}{{n(S)}}$
Probability = $\dfrac{{{K^n} - {{\left( {K - 1} \right)}^n}}}{{{N^n}}}$
∴Option (D) is correct
Note: There are some main rules associated with basic probability:
1. P(not A)=1-P(A)
2. P(A or B)=P(event A occurs or event B occurs or both occur)
3. P(A and B)=P(both event A and event B occurs)
4. The general Addition Rule: P(A or B) = P(A) + P(B) – P(A and B)
Recently Updated Pages
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Why Are Noble Gases NonReactive class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let X and Y be the sets of all positive divisors of class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x and y be 2 real numbers which satisfy the equations class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x 4log 2sqrt 9k 1 + 7 and y dfrac132log 2sqrt5 class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x22ax+b20 and x22bx+a20 be two equations Then the class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Trending doubts
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
At which age domestication of animals started A Neolithic class 11 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Which are the Top 10 Largest Countries of the World?
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give 10 examples for herbs , shrubs , climbers , creepers
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference Between Plant Cell and Animal Cell
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Write a letter to the principal requesting him to grant class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Change the following sentences into negative and interrogative class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Fill in the blanks A 1 lakh ten thousand B 1 million class 9 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)