Venn Diagram for the maximum of the two numbers which is greater than four.

Question

Two dies are tossed and the outcome is the maximum of the two numbers which is greater than four.

The following doesn't make any sense to me as it doesn't explain the scenario clearly:

The following makes sense to me, but doesn't look very efficient:

How can I draw a Venn Diagram to represent the above random experiment?

Answer 1

The intersection of the two circles, otherwise known as the union, is the number any of the die need to win. It is represented as the union because only one of the 2 die have to get a 5 or a 6 to win. It is like throwing 2 darts at the Venn Diagram, each within one of the circles, and if at least one of the darts hits the union (dark blue), you win.

Answer 2

This is not a conventional Venn diagram in the sense that there is no 1-1 correspondence between an element of the bubbles and an outcome. But it is still a relevant graphical representation of the different situations: the two colours represent the two dice, and either both dice give our a number larger than $5 $, which corresponds to the zone in the middle (both colours larger thafn $5 $) or one die gives a number less than $5 $, but in this case the other can't be also less than $5 $. This is depicted by the fact that there is no intersection between the zone where Blue $<5 $ and the zone purple $<5 $.

Edit: a clearer way would be to write "First die greater than $5 $" in the first bubble and similarly "second..." in the other one, and the intersection would naturally be the case when both dice give out numbers larger than $5 $.

Answer 3

You need to visualize the union, not the intersection when dealing with this experiment.

From this diagram it is easy to compute the total number of combinations giving the required outcome (greater than four): $2 \times 4 + 2 \times 2 + 4 \times 2 = 20$.

Answer 4

Here is another look at it:

$\hspace{3cm}$

Key: $(1,*)\cap (*,5)=(1,5)$.