Question

A box contains 4 green and 2 blue dice. Three dice are chosen after the other. Deternmine the values of randombvariable G representing the number of green dice. ​

Answer 1

Answer:

So the random variable, g, will be

1 with p=1/5, 2 with p=3/5, 3 with p=1/5

Hope it helps!!

Answer 2

The values of random variable G represents  the number of green dice  $P(X=1)=\frac{1}{5}$  ,$P(X=2)=\frac{3}{5}$   and  $P(X=3)=\frac{1}{5}$ .

Step-by-step explanation:

Given:

4 green and 2 blue dice are in box.

3 dice are chosen after the other.

To Find:

the values of random variable G represents the number of green dice

Formula Used:

The random variable G assume the values k 1, k 2, …with corresponding probability P (X=k 1), P (X=k 2),…

Solution:

As given - 4 green and 2 blue dice are in box.3 dice are chosen after the other.

Let G denotes random variable which is number of representing the number of green dice

The possible values of G are 1,2, and 3

P(G=1)

The probability  to get  1 green dice with  2 blue dice =

$\frac{( 4X2X1)}{(6X5X4)} =\frac{1}{15}$

There are 3  positions  to get  1 green die (GBB, BGB, BBG)

Hence  total probability  to get  1 green is   $3X\frac{1}{15} =\frac{3}{15} =\frac{1}{5}$ .

P(G=2)

The probability  to get  2 green followed by 1 blue  =          

$\frac{( 4X3X2)}{(6X5X4)} =\frac{1}{5}$

There are 3  positions  to get  2 green die (GGB, BGG, GBG)

P(G=2)= Hence  total probability  to get  2 green is  $3X\frac{1}{5} =\frac{3}{5}$.

P(G=3)

The probability  to get  3  green     $=\frac{( 4X3X2)}{(6X5X4)} =\frac{1}{5}$

There are 1 positions  to get GGG;

Hence   P(G=3) =total probability  to get  3 green is    $1X\frac{1}{5} =\frac{1}{5}$ .

Thus, The values of random variable G representing the number of green dice $P(X=1)=\frac{1}{5}$  ,$P(X=2)=\frac{3}{5}$   and  $P(X=3)=\frac{1}{5}$ .