Both sixes, given one
Two fair dice are rolled, and you are told that at least one of them shows a six. What is the probability that both show a six?
Fractions, decimals with at least 3 significant digits, and expressions such as sqrt(2)/2, e^-1 or pi/4.
List the equally likely outcomes that have at least one six.
There are 11 of them.
h
s Shown after a correct answer. Revealing it first marks the problem as seen, not solved.
Idea. Condition by counting: keep the outcomes compatible with the information and see how many of them have two sixes.
Step 1. Of the 36 equally likely ordered outcomes, those with at least one six are: 6 with the first die showing six, 6 with the second, minus the double six counted twice: 11.
Step 2. Only one of them, (6, 6), has two sixes.
Step 3.
The trap. Answering , as if you had been told that a particular die, say the first one, shows a six. “At least one” is weaker information, and it leaves more outcomes in play.