Answer :
We are asked to determine the probability of getting an odd number and then getting a number greater than 3 when rolling a dice.
To do that we will use the following relationship:
[tex]P(\text{odd and >3)=P(odd)P(>3)}[/tex]This means that we need to determine the product of each individual probability.
The probability of getting an odd number is determined by dividing the total number of desired outcomes over the total number of outcomes. There are 3 odd numbers in a 6 sided dice:
[tex]1,3,5[/tex]Therefore, the probability of getting an odd number is:
[tex]P(\text{odd)}=\frac{3}{6}=\frac{1}{2}[/tex]Now, there are 3 numbers greater than three, these are:
[tex]4,5,6[/tex]Therefore, the probability of getting a number greater than 3 is:
[tex]P(>3)=\frac{3}{6}=\frac{1}{2}[/tex]Therefore, the total probability is:
[tex]P(\text{odd and >3)=}(\frac{1}{2})(\frac{1}{2})=\frac{1}{4}[/tex]Therefore, the probability is 1/4 or 25%.