Question

Roll a fair, six-sided die. Let A = a prime number of dots is rolled. Let B = an odd number of dots is rolled. Then A = {2, 3, 5} and B = {1, 3, 5}. Therefore, A AND B = {3, 5}. A OR B = {1, 2, 3, 5}. The sample space for rolling a fair die is S = {1, 2, 3, 4, 5, 6}. Draw a Venn diagram representing this situation.

Short answer

The Venn diagram is as follows:

Step-by-step solution

Given Information

Roll a fair, six-sided die. Let A= a prime number of dots is rolled. Let B= an odd number of dots is rolled. Then $A=\{2,3,5\}$and $B=\{1,3,5\}$. Therefore, $AANDB=\{3,5\}$and $ARB=\{1,2,3,5\}$. The sample space for rolling a fair die is $S=\{1,2,3,4,5,6\}$.

Calculation

We have

Sample space for rolling a fair die is $S=\{1,2,3,4,5,6\}$

Event A= a prime number of dots is rolled

Event B= an odd number of dots is rolled.

$\begin{array}{r}A=\{2,3,5\}\\ B=\{1,3,5\}\\ AANDB=\{3,5\}\\ AORB=\{1,2,3,5\}\end{array}$

Thus, Venn diagram is as follows

Conclusion

Hence, the Venn diagram representing the situation is sketched.