A die is rolled. What is the probability of rolling an even number given that th
Practice Questions
Q1
A die is rolled. What is the probability of rolling an even number given that the number rolled is greater than 2?
1/2
1/3
1/4
2/3
Questions & Step-by-Step Solutions
A die is rolled. What is the probability of rolling an even number given that the number rolled is greater than 2?
Correct Answer: 2/3
Step 1: Identify the total possible outcomes when a die is rolled. The outcomes are {1, 2, 3, 4, 5, 6}.
Step 2: Determine the outcomes that are greater than 2. These outcomes are {3, 4, 5, 6}.
Step 3: Identify which of these outcomes are even numbers. The even numbers in {3, 4, 5, 6} are {4, 6}.
Step 4: Count the total number of outcomes greater than 2. There are 4 outcomes: 3, 4, 5, and 6.
Step 5: Count the number of even outcomes among those greater than 2. There are 2 even outcomes: 4 and 6.
Step 6: Calculate the probability of rolling an even number given that the number rolled is greater than 2. This is done by dividing the number of even outcomes (2) by the total outcomes greater than 2 (4).
Step 7: The probability is 2 divided by 3, which simplifies to 2/3.
Conditional Probability – The probability of an event occurring given that another event has already occurred.
Sample Space Reduction – Narrowing down the sample space based on given conditions.
Even and Odd Numbers – Understanding the classification of numbers as even or odd.
