# One die and 1, 2 or 3 coins

**Discrete Mathematics**Level 3

A fair die is tossed.

If the die lands on 1, 2 or 3, then 3 fair coins are tossed.

If the die lands on 4 or 5, then 2 fair coins are tossed.

If the die lands on 6, then 1 fair coin is tossed.

If the die lands on 1, 2 or 3, then 3 fair coins are tossed.

If the die lands on 4 or 5, then 2 fair coins are tossed.

If the die lands on 6, then 1 fair coin is tossed.

Given that the resulting coin tosses produced no tails, what is the probability that the die landed on 6?

The probability can be expressed as \( \dfrac ab\) for coprime positive integers \(a\) and \(b\), find the value of \(a+b\).

###### Image Credit: Flickr nickphotos.

**Your answer seems reasonable.**Find out if you're right!

Sign up to access problem solutions.

**That seems reasonable.**Find out if you're right!

Already have an account? Log in here.