A single 6-sided die is rolled twice.
C. Find the odds in favor of getting 2 numbers whose sum is greater than 5.
I would simply like to be shown the steps to work this problem.
Thank you so much David Q/R.
To get it right, make sure you distinguish between the first and second throw. If you do that, you'll see that there are 36 distinct outcomes: (1, 1), (1, 2), (1, 3), ... (6, 4), (6, 5) and (6, 6). They're all equally likely with probability 1/36, so how many of them total more than 5? We could just enuerate them all - or better, work out how many total five or less (because there are fewer of them), and then subtract the probability from 1. These are: (1, 1), (1, 2), (1, 3), (1, 4), (2, 1), (2, 2), (2, 3), (3, 1), (3, 2) and (4, 1). There are 10 of them, so I reckon the answer ought to be 1 - (10/36) = 0.72. Do you agree?
You're welcome!
To find the odds in favor of getting 2 numbers whose sum is greater than 5 when rolling a single 6-sided die twice, follow these steps:
Step 1: Determine the favorable outcomes
To find the favorable outcomes, list all possible combinations of two numbers when rolling a 6-sided die twice. For example, if we denote a die roll as (a, b), where a is the first roll and b is the second roll, the favorable outcomes would be all the combinations where the sum of the two numbers is greater than 5.
Favorable outcomes: (6, 1), (6, 2), (6, 3), (6, 4), (5, 2), (5, 3), (5, 4), (4, 3), (4, 4), (3, 4), (6, 6)
Step 2: Determine the total number of outcomes
To find the total number of outcomes, consider that each die can have 6 possible outcomes (numbers 1 to 6) and there are two dice being rolled. Therefore, the total number of outcomes is 6 * 6 = 36.
Total number of outcomes: 36
Step 3: Calculate the odds in favor
The odds in favor are calculated by dividing the number of favorable outcomes by the total number of outcomes.
Odds in favor = (Number of favorable outcomes) / (Total number of outcomes)
Odds in favor = 11 (favorable outcomes) / 36 (total outcomes)
So, the odds in favor of getting 2 numbers whose sum is greater than 5 when rolling a single 6-sided die twice is 11/36.
Note: The odds are traditionally written in the form of "x:y" or "x to y," where x represents the number of favorable outcomes and y represents the number of unfavorable outcomes. In this case, the odds in favor is represented as "11:25" or "11 to 25" (since there are 25 unfavorable outcomes).