Lat night I was flipping through Art of Problem Solving’s *Intermediate Counting and Probability* book and found a couple of ideas that looked like fun problems to talk through with kids. Today we talked about two of them for our family math project.

The first problem is about rolling dice. You throw two six-sided dice and all you know is that neither one shows a 6. What is the probability that the sum is equal to 8? It was interesting to hear their approach to this problem since we haven’t talked about probability in a couple of months:

The next problem was about flipping coins. You play a game that involves taking turns flipping two (fair) coins at the same time. The game ends on a turn where there is at least one head showing. When the game ends, what is the probability that the other coin was also a head?

As with the last problem, it was interesting to hear the ideas that the kids had for this one. My older son guessed that the answer would be 1/2 and my younger son guessed 1/4. I think that it was a little more difficult for them to understand the right answer on this one (compared to the first problem), but we did eventually get there.

So a fun morning talking about some introductory probability problems. I like both of these problems because they are easy to understand even though they both have slightly surprising answers. Hearing the expected solutions and then getting to the actual solutions made for a great morning math talk with the boys.