If you roll a die twice, what is the probability of getting the same number both

₹0.0

Question: If you roll a die twice, what is the probability of getting the same number both times?

Options:

Correct Answer: 1/36

Solution:

There are 6 outcomes where the same number appears (1-1, 2-2, etc.) out of 36 total outcomes, so the probability is 6/36 = 1/6.

If you roll a die twice, what is the probability of getting the same number both times?

If you roll a die twice, what is the probability of getting the same number both times?

Step 1: Understand that a die has 6 sides, numbered from 1 to 6.
Step 2: When you roll a die twice, each roll can result in any of the 6 numbers.
Step 3: Calculate the total number of outcomes when rolling the die twice. Since there are 6 options for the first roll and 6 options for the second roll, multiply them: 6 * 6 = 36 total outcomes.
Step 4: Identify the outcomes where the same number appears on both rolls. These outcomes are (1-1), (2-2), (3-3), (4-4), (5-5), and (6-6). There are 6 such outcomes.
Step 5: To find the probability of getting the same number both times, divide the number of favorable outcomes (6) by the total number of outcomes (36): 6/36.
Step 6: Simplify the fraction 6/36 to get 1/6.

Probability of Independent Events – The question tests the understanding of calculating probabilities for independent events, specifically the likelihood of rolling the same number on two separate rolls of a die.
Sample Space – It assesses the ability to identify the total number of possible outcomes when rolling a die twice, which is crucial for calculating probabilities.