If you roll two dice, what is the probability of rolling a 3 and an even number?
The probability of rolling a 3 is
The probability of rolling an even number is
Therefore by the multiplication principle, the probability of both the one and the other event occurring is
This is when you first roll a 3 and then an even number.
The probability of first rolling an even number and then a 3 is exactly the same.
So the probability of rolling a 3 and an even number (in whatever order) are (adding the chances now):