Question

which formula gives the probability distribution shown by the table?
a. P(X) = 1/X
b. P(X) = X/6
c. P(X) = 6/X
d. P(X) = 1/6

Answer 1

The formula which gives the probability distribution shown by the table is P(X) = 1/X

Given :

The table

$\begin{gathered} \begin{array}{|c|c| c|c| } \sf{X} & \sf 2& \sf 3& \sf 6 \\ \\ \sf P(X) & \dfrac{1}{2} & \dfrac{1}{3} & \dfrac{1}{6} \end{array}\end{gathered}$

To find :

The formula which gives the probability distribution shown by the table is

a. P(X) = 1/X

b. P(X) = X/6

c. P(X) = 6/X

d. P(X) = 1/6

Solution :

Step 1 of 2 :

Write down the given table

The given table is

$\begin{gathered} \begin{array}{|c|c| c|c| } \sf{X} & \sf 2& \sf 3& \sf 6 \\ \\ \sf P(X) & \dfrac{1}{2} & \dfrac{1}{3} & \dfrac{1}{6} \end{array}\end{gathered}$

Step 2 of 2 :

Find the formula which gives the probability distribution shown by the table

From the table we observe that

$\displaystyle \sf{ \sum P(X) = \frac{1}{2} + \frac{1}{3} + \frac{1}{6} = 1 }$

Which states that P(X) gives probability distribution function

Now from the given table

$\displaystyle \sf{ 2.P(2) = 1 }$

$\displaystyle \sf{ 3.P(3) = 1 }$

$\displaystyle \sf{ 6.P(6) = 1 }$

Thus we have

$\displaystyle \sf{ X.P(X) = 1 }$

$\displaystyle \sf{ \implies P(X) = \frac{1}{X} }$

Hence the correct option is a. P(X) = 1/X