What is the probability of rolling first an odd number then

What is the probability of rolling first an odd number, then an even number with one fair die?

1/2

1/3

1/4

1/6

Solution

Sample space = All possible outcomes = {1,2,3,4,5,6}

Odd number on a dice are - 1,3,5

And the even number on the dice are - 2,4,6

So, probability of rolling an odd number first = probability of getting any of the values {1,3,5} in first roll = 3/6 = 1/2.

Probability of rolling an even number in the second roll = probability of getting any of the values {2,4,6} in the second roll = 3/6 = 1/2.

So, the probability of getting an odd in the first roll and an even in the second will be the multiplication of the above two cases as the two events are independent of each other. That means the occurence of an odd number doesn\'t affect the occurence of an even number in the second roll.

So, required probability = 1/2 * 1/2 = 1/4.

So, option (C) is correct.