Suppose that a fair die is rolled 9 times b Find the probabi

Suppose that a fair die is rolled 9 times.

(b) Find the probability that 1 and 2 together appear three times, 3 and 4 together four times, 5

once and 6 once.

Probability Theroy - please show all work

Solution

(b)

Find the probability that 1 and 2 together appear three times, 3 and 4 together four times, 5

once and 6 once.

We need follwoing outcome when a fair die is rolled 9 times:

1,2,1,2,1,2,3,4,3,4,3,4,3,4,5,6

For the above output, we need to roll die at least 16 times. So in 9 rolls above output is not possible. Therefore it is impossible event is given situation. So the required probablity is 0.