Roll 2 standard dice and add the numbers. whats the probability of getting a number Larger than 4 for the first time on the third roll?
To determine the probability of getting a number larger than 4 for the first time on the third roll when rolling two standard six-sided dice, we can break the problem into smaller steps.
Step 1: Find the total number of possible outcomes when rolling two dice. Each die has 6 faces, so the total number of outcomes is 6 multiplied by 6, which is 36.
Step 2: Identify the favorable outcomes. In this case, we want to know the probability of getting a number larger than 4 on the third roll for the first time. So, we need to figure out the favorable outcomes for this specific scenario.
To do this, we can refer to the possible outcomes on each roll:
- On the first roll, the numbers larger than 4 are 5 and 6, giving us 2 favorable outcomes.
- On the second roll, if the first roll resulted in a number smaller than or equal to 4, we have 4 favorable outcomes (5 or 6), as these would be larger than 4 for the first time.
- On the third roll, if both the first and second rolls resulted in numbers smaller than or equal to 4, any number on the third roll would satisfy the condition of being larger than 4 for the first time. So, there are 6 favorable outcomes for the third roll.
Step 3: Calculate the probability. To find the probability, divide the number of favorable outcomes by the total number of possible outcomes:
Favorable outcomes = 2 favorable outcomes (first roll) + 4 favorable outcomes (second roll) + 6 favorable outcomes (third roll) = 12
Probability of getting a number larger than 4 for the first time on the third roll = Favorable outcomes / Total number of possible outcomes = 12 / 36 = 1/3
Therefore, the probability of getting a number larger than 4 for the first time on the third roll is 1/3.