Answer

Verified

419.7k+ views

Hint: Here we will apply the property of the probability i.e. Sum of all probabilities is equal to one.

Complete step-by-step answer:

In a probability distribution the sum of all probabilities is equal to one.

$ \Rightarrow \sum\limits_{x = 0}^n {P(x)} = 1$

Here, n=8. Therefore,

$

\Rightarrow \sum\limits_{x = 0}^8 {P(x)} = a + 3a + 5a + 7a + 9a + 11a + 13a + 15a + 17a = 1 \\

\Rightarrow 81a = 1 \\

\Rightarrow a = \dfrac{1}{{81}} \\

$

Now it is given that $a = \dfrac{1}{k}$

$ \Rightarrow \dfrac{1}{{81}} = \dfrac{1}{k}$

So on comparing $k = 81$.

Note: In such types of questions the key concept we have to remember is that the sum of the probability distribution is always 1 so, simply add all the probabilities and equate to 1.Probability for a particular value or range of values must be between 0 and 1.

Complete step-by-step answer:

In a probability distribution the sum of all probabilities is equal to one.

$ \Rightarrow \sum\limits_{x = 0}^n {P(x)} = 1$

Here, n=8. Therefore,

$

\Rightarrow \sum\limits_{x = 0}^8 {P(x)} = a + 3a + 5a + 7a + 9a + 11a + 13a + 15a + 17a = 1 \\

\Rightarrow 81a = 1 \\

\Rightarrow a = \dfrac{1}{{81}} \\

$

Now it is given that $a = \dfrac{1}{k}$

$ \Rightarrow \dfrac{1}{{81}} = \dfrac{1}{k}$

So on comparing $k = 81$.

Note: In such types of questions the key concept we have to remember is that the sum of the probability distribution is always 1 so, simply add all the probabilities and equate to 1.Probability for a particular value or range of values must be between 0 and 1.

Recently Updated Pages

Basicity of sulphurous acid and sulphuric acid are

Assertion The resistivity of a semiconductor increases class 13 physics CBSE

The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths

What is the stopping potential when the metal with class 12 physics JEE_Main

The momentum of a photon is 2 times 10 16gm cmsec Its class 12 physics JEE_Main

Using the following information to help you answer class 12 chemistry CBSE

Trending doubts

First census of India was done in A 1871 1881 B 1911 class 12 biology CBSE

Difference Between Plant Cell and Animal Cell

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

How many lightyears away is the sun from the earth class 6 social science CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Change the following sentences into negative and interrogative class 10 english CBSE

Name 10 Living and Non living things class 9 biology CBSE

List some examples of Rabi and Kharif crops class 8 biology CBSE