Question

1. Suppose that two fair dice are rolled. Find the probability that the number on the first die is a 6 or the number on the second die is a 2.

Answer 1

Two fair die are rolled.

We have to find the probability that the number on the first die is a 6 or the number on the second die is 2.

First, we note that

The first die can show 6 outcomes.

The second die can show 6 outcomes.

So, the total number of outcomes that can result from the rolling of the two dice, is 6*6, ie. 36.

The all possible number of cases is 36.

Now, the first die can show a 6, in 6 ways; this is beacuse in that case, the first die would show 6 and the second die can show any of the 6 outcomes.

Now, the second die can show a 2, in 6 ways; this is beacuse in that case, the first die would show any of the 6 outcomes and the second die will show 2.

And, both the first die will show 6 and the second die will show 2, in only 1 way.

Now,

P(First die 6 or Second die 2)

=P(First die 6)+P(Second die 2)-P(First die 6 and second die 2)

The answer is

The probability that the number on the first die is a 6 or the number on the second die is a 2, is 0.3056 approximately.