If two fair dice are rolled, find the odds in favor of getting doubles
Size of sample space = 6*6 = 36
Number of doubles in the sample space = 6
Odd = number of times in favour of ÷ number times against
= 6 ÷ (36-6)
= 6 ÷ 30
= 1/5
To determine the odds in favor of getting doubles when two fair dice are rolled, we first need to find the total number of possible outcomes and then the favorable outcomes.
1. Total number of possible outcomes:
Since two dice are rolled, each die has 6 possible outcomes (from 1 to 6), and there are a total of 6 * 6 = 36 possible outcomes when two dice are rolled.
2. Favorable outcomes:
To get doubles, both dice must show the same number when rolled. There are six possible ways to obtain doubles: (1, 1), (2, 2), (3, 3), (4, 4), (5, 5), and (6, 6).
3. Odds in favor of getting doubles:
The odds in favor of an event are given by the ratio of favorable outcomes to total outcomes. Therefore, the odds in favor of getting doubles when two fair dice are rolled can be calculated as:
Number of favorable outcomes / Number of possible outcomes
In this case, the number of favorable outcomes is 6 (as we found in step 2), and the number of possible outcomes is 36 (as we found in step 1). Therefore, the odds in favor of getting doubles are:
6 / 36 = 1/6
So the odds in favor of getting doubles when two fair dice are rolled are 1/6.