A die is rolled. What is the probability of rolling an even number given that the number rolled is greater than 2?
Practice Questions
1 question
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
The possible outcomes greater than 2 are {3, 4, 5, 6}. The even numbers among these are {4, 6}. Thus, the probability is 2/3.
Questions & Step-by-step Solutions
1 item
Q
Q: A die is rolled. What is the probability of rolling an even number given that the number rolled is greater than 2?
Solution: The possible outcomes greater than 2 are {3, 4, 5, 6}. The even numbers among these are {4, 6}. Thus, the probability is 2/3.
Steps: 7
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.
