Question

The four faces of a regular tetrahedron are marked $A,B,C$ and $D$ and it is thrown twice.

1. Write all the possible outcomes namely $AA,AB,$ etc.
2. How many outcomes are there in all?
3. How many outcomes are there with both the letters are the same?

Answer 1

Step 1: Finding possible outcomes

It is given that the faces of a tetrahedron are marked with letters $A,B,C$ and $D$.

There are two throws.

So the sample space showing the combinations can be represented as below.

Step 2: Finding the number of outcomes

On counting from the table, the total number of outcomes are $16$.

Step 3: Finding outcomes with both letters being the same

Highlighting the outcomes having both letters the same,

So, there are four outcomes where both letters are the same.