A pair of 6 sided fair dice are rolled. If one of the dice shows an odd number what is the probability of the sum of the dice being 7 ?
To find the probability of the sum of the dice being 7 given that one of the dice shows an odd number, we need to determine the number of favorable outcomes and the total number of possible outcomes.
First, let's calculate the number of favorable outcomes. If one of the dice shows an odd number, there are three possibilities: (1, 6), (3, 4), and (5, 2). These pairs of numbers have a sum of 7, so we have three favorable outcomes.
Next, let's find the total number of possible outcomes. Since we are rolling a pair of 6-sided dice, each die has six possible outcomes. Therefore, the total number of outcomes is 6 * 6 = 36.
Now, we can calculate the probability by dividing the number of favorable outcomes by the total number of possible outcomes.
Probability = Number of Favorable Outcomes / Number of Possible Outcomes
= 3 / 36
= 1 / 12
Therefore, the probability of the sum of the dice being 7 given that one of the dice shows an odd number is 1/12.
1 -- * * * * * 6
3 -- * * * 4 * *
5 -- * 2 * * * *
3/(3*6 ) = 1/6