A pair of dice are rolled find the following, a) the probability of doubles, b) the odds in favor of a sum greater than 2, c) the probability of sum that is even and less than 5
Again, either-or probabilities are found by adding the individual probabilities. Each combination of the die has a 1/36 probability.
a) What are the possible number of doubles? Follow the rule above.
b) This is the same as 1-probability of getting 2 or less with two die.
c) How many ways can you get 2 or 4? Divide that by 36.
To find the answers to these questions, we need to understand the total possible outcomes and the favorable outcomes for each case.
a) Probability of doubles:
To find the probability of rolling doubles, we need to determine the number of favorable outcomes and the total number of possible outcomes. In this case, the favorable outcomes are when both dice show the same number (1-1, 2-2, 3-3, 4-4, 5-5, 6-6). There are 6 favorable outcomes.
The total number of possible outcomes when rolling two dice is 6 * 6 = 36, as each die has 6 sides. So, the probability of rolling doubles is 6/36 or simplified to 1/6.
b) Odds in favor of a sum greater than 2:
To determine the odds in favor of a sum greater than 2, we need to compare the number of favorable outcomes to the number of unfavorable outcomes. In this case, a sum greater than 2 means rolling any number from 3 to 12.
To find the number of favorable outcomes, we can list all the combinations that result in a sum greater than 2: (1-2, 1-3, 1-4, 1-5, 1-6, 2-1, 2-3, 2-4, 2-5, 2-6, 3-1, 3-2, 3-4, 3-5, 3-6, 4-1, 4-2, 4-3, 4-5, 4-6, 5-1, 5-2, 5-3, 5-4, 5-6, 6-1, 6-2, 6-3, 6-4, 6-5). There are 30 favorable outcomes.
To find the number of unfavorable outcomes, we need to find the total number of outcomes and subtract the number of favorable outcomes. The total number of possible outcomes is still 6 * 6 = 36. So, the number of unfavorable outcomes is 36 - 30 = 6.
Therefore, the odds in favor of a sum greater than 2 are 30:6, which can be further simplified to 5:1.
c) Probability of a sum that is even and less than 5:
To find the probability of rolling a sum that is even and less than 5, we need to determine the number of favorable outcomes and the total number of possible outcomes. In this case, the favorable outcomes are (1-1, 1-3, 2-2, 2-4, 3-1, 3-3, 4-2). There are 7 favorable outcomes.
To find the total number of possible outcomes, we still use 6 * 6 = 36.
So, the probability of rolling a sum that is even and less than 5 is 7/36.