Understanding Conditional Probability with Dice Rolls

 

What is the conditional probability that the first die is six given that the sum of the dice is seven? 

Conditional probability is the probability of an event occurring given that another event has already happened. In this scenario, the event of interest is the first die being a six, given that the sum of the dice is seven.

When rolling two dice, there are a total of 36 possible outcomes. The possible sums of the dice are 2 to 12, with the sum of 7 being the most likely outcome (occurring six times out of 36 possible outcomes).

To find the conditional probability that the first die is six given that the sum of the dice is seven, we must consider the number of times that the first die being a six results in a sum of seven. This can only occur when the second die is one. So, there is only one outcome (6,1) that results in a sum of seven and a first die value of six.

Hence, the conditional probability that the first die is six given that the sum of the dice is seven is 1/6. This means that if the sum of the dice is seven, there is only a 1 in 6 chance that the first die is six.

In conclusion, understanding conditional probability is important in determining the likelihood of an event occurring given that another event has already happened. In this scenario, we have calculated the conditional probability that the first die is six given that the sum of the dice is seven and found it to be 1/6.