Question

Bob throws a fair four-sided die, after which Alice throws a fair and independent six-sided die. What is the probability that they obtain the same number?

Answer 1

Answer: 1/6.

Explanation:

The possible outcomes of Bob are {1, 2, 3, 4}

The possible outcomes of Alice are {1, 2, 3, 4, 5, 6}

Notice that the outcome space of Bob is included in the outcome space of Alice.

Now, Bob rolls his dice and gets an outcome between 1 and 4, let's suppose that the outcome is a 2.

Now, Alice needs to roll a 2 in her 6-sided dice.

The 2 appears one time, and there are 6 possible outcomes:

The probability will be equal to the probability for each number, this i:

P = 1/6.

And will be the same for any outcome in Bob's roll, so the probability that they obtain the same number is 1/6.