Question

A single six-sided die is rolled twice. What is the probability of rolling an odd number on the first roll and an odd number on the second roll?

Answer 1

Answer:

$\frac{1}{2}$

Step-by-step explanation:

in a die there are three odd and three even numbers. therefore the probability if getting an odd or even number will always be half. rolling the same die twice for odd number will have an outcome of $\frac{6}{12}$ that's the same as half.

Answer 2

Given:

It is given that a single six-sided die is rolled twice.

To Find:

The probability of getting an odd number in both the rolls.

Solution:

The given problem can be solved by using the concepts of probability.

1. It is given that the die is rolled twice. Therefore, the possible outcomes are as follows;

Assuming (x,y) where x is the outcome of the first roll and y is the outcome of the second roll the 36 possibilities are:

• ( 1, 1) , ( 1, 2) , ( 1, 3) , ( 1, 4) , ( 1, 5) , ( 1, 6),

• ( 2, 1) , ( 2, 2) , ( 2, 3) , ( 2, 4) , ( 2, 5) , ( 2, 6),

• ( 3, 1) , ( 3, 2) , ( 3, 3) , ( 3, 4) , ( 3, 5) , ( 3, 6),

• ( 4, 1) , ( 4, 2) , ( 4, 3) , ( 4, 4) , ( 4, 5) , ( 4, 6),

• ( 5, 1) , ( 5, 2) , ( 5, 3) , ( 5, 4) , ( 5, 5) , ( 5, 6),

• ( 6, 1) , ( 6, 2) , ( 6, 3) , ( 6, 4) , ( 6, 5) , ( 6, 6).

2. It is given that an odd outcome is recorded and both the first roll and the second roll. Therefore, the favorable outcomes are as follows;

• (1, 3) , (1 , 3) , ( 1, 5),

• (3, 1) , (3, 3) , ( 3, 5),

• (5, 1) , (5, 3) , ( 5, 5).

3. The total number of outcomes is 36, and the favorable number of outcomes is 9.

4. Probability of an event happening is defined as the total number of favorable outcomes divided by the total number of outcomes. It is formulated as:

• Probability of an event (E) = (total favorable outcomes / total number of outcomes)

5. In the given question the total number of outcomes is 36 and the favorable number of outcomes is 9, therefore the probability is given by,

• Probability of odd number in both the rolls =$\frac{9}{36}$,

=> 9/36 = $\frac{1}4}$.

Therefore, the probability of rolling odd numbers for both the first and second rolls is 1/4.