Question

Consider a prismatic dice with sides 1, 2, 3, and 4. When rolled, P(1) = 1/10 , P(2) = 2/10 , P(3) = 3/10 , P(4) = 4/10What is the probability of getting an odd outcome on either of two rolls of the dice?

Answer 1

Solution:

Given:

A prismatic dice with sides 1,2,3, and 4.

Where when rolled

$\begin{gathered} P(1)=\frac{1}{10} \\ P(2)=\frac{2}{10} \\ P(3)=\frac{3}{10} \\ P(4)=\frac{4}{10} \end{gathered}$

The probability of getting an odd outcome on either of two rolls of the dice is expressed as

$P(odd\text{ outcome on either of two rolls\rparen=P\lparen1 and 2\rparen or P\lparen1 and 4\rparen or P\lparen3 and 2\rparen or P\lparen3 and 4\rparen}$

Thus, we have

$\begin{gathered} P(odd\text{ outcome on either of two rolls\rparen = \lparen}\frac{1}{10}\times\frac{2}{10})+(\frac{1}{10}\times\frac{4}{10})+(\frac{3}{10}\times\frac{2}{10})+(\frac{3}{10}\times\frac{4}{10}) \\ =\frac{1}{50}+\frac{1}{25}+\frac{3}{50}+\frac{3}{25} \\ =\frac{6}{25} \end{gathered}$

Hence, the probability of getting an odd outcome on either of two rolls of the dice is evaluated to be

$\frac{6}{25}$