two dice are rolled, find the probability that an even number appears on the first and the number 5 appears on the second die

1/36

Step-by-step explanation:

Two dice are rolled.

Find the probability that;

An even number appears on the first and, The number 5 appears on the second die

Since the two dice are rolled simultaneously, there are 36 possible outcomes:

1,1 1,2 1,3 1,4 1,5 1,6 (six outcomes)

2,1 2,2 2,3 2,4 2,5 2,6 (another six outcomes)

3,1 3,2 3,3 3,4 3,5 3,6 (six outcomes)

4,1 4,2 4,3 4,4 4,5 4,6 (six outcomes)

5,1 5,2 5,3 5,4 5,5 5,6 (six outcomes)

6,1 6,2 6,3 6,4 6,5 6,6 (six outcomes finally!)

So six by 6 is 36 outcomes

For an even number to appear on dice one, either number 2, number 4 or number 6 should apear (even numbers between 1 and 6)

The probability that an even number appears on the first die is 6/36 = 1/6

The probobility that the number 5 appears on the second die is 6/36 = 1/6

The probability that an even number appears on the first die and the number 5 appears on the second die is;

1/6 * 1/6 = 1/36

* Remember that we multiply wherever there is an 'AND' in probability!