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
To calculate the probabilities and odds in these scenarios, we need to first determine the sample space and the favorable outcomes.
The sample space for rolling two dice consists of all possible combinations when rolling each die. Since each die has six sides, there are 6 possible outcomes for each die. Therefore, the total number of outcomes in the sample space is 6 x 6 = 36.
a) Probability of doubles:
To find the probability of getting doubles, we need to determine the number of favorable outcomes, which is the number of outcomes where both dice show the same number. In this case, there are 6 possible outcomes: (1, 1), (2, 2), (3, 3), (4, 4), (5, 5), and (6, 6). Therefore, the probability of getting doubles is 6/36.
b) Odds in favor of a sum greater than 2:
To find the odds in favor of a sum greater than 2, we need to identify the number of favorable outcomes and the number of unfavorable outcomes. In this case, a sum greater than 2 can be obtained with any combination of the two dice except (1, 1) because it adds up to 2. So there are 35 favorable outcomes out of the total 36 outcomes. The odds in favor can be expressed as 35:1.
c) Probability of a sum that is even and less than 5:
To calculate the probability of getting a sum that is even and less than 5, we need to find the number of favorable outcomes.
The possible outcomes that satisfy this condition are: (1, 1), (1, 3), (2, 2), (2, 4), (3, 1), (3, 3), (4, 2), and (4, 4). There are 8 favorable outcomes out of the total 36 outcomes. Therefore, the probability is 8/36.
Remember, to find probabilities, we divide the number of favorable outcomes by the total number of outcomes, and to find odds, we compare the number of favorable outcomes to the number of unfavorable outcomes.