Respuesta :
Let's begin by listing out the given information:
A fair dice has 6 sides
The dice has its sides numbered from 1-6
The number of sides with even numbers (2, 4 & 6) equals 3
The number of sides with odd numbers (1, 3 & 5) equals 3
The probability of rolling an even number is given as shown below:
[tex]\begin{gathered} P=\frac{Number\text{ of Possible Outcome}}{Total\text{ Number of Outcome}} \\ P\mleft(even\mright)=\frac{3}{6}=\frac{1}{2} \\ P(even)=\frac{1}{2} \end{gathered}[/tex]The probability of rolling an odd number is given as shown below:
[tex]\begin{gathered} P=\frac{Number\text{ of Possible Outcome}}{Total\text{ Number of Outcome}} \\ P(odd)=\frac{3}{6}=\frac{1}{2} \\ P(odd)=\frac{1}{2} \end{gathered}[/tex]The probability of rolling an even number followed by an odd number is obtained by the product of the probabilities above. We have:
[tex]\begin{gathered} P(even,odd)=P(even)\times P(odd) \\ P(even,odd)=\frac{1}{2}\times\frac{1}{2}=\frac{1}{4} \\ P(even,odd)=\frac{1}{4} \end{gathered}[/tex]Therefore, the probability of rolling an even number and then an odd number is 1/4
