AND Probability

Question

1)You want to find the probability of rolling a sum of 9 on two dice and then rolling a sum of 3 on the next roll. Tell whether these events are independent or dependent.


Calculate the probability.

(Round to three decimal places.)



2)You are going to draw two candy bars from a large bag containing 21 Snickers bars and 6 Twix bars. What is the probability that both candy bars you draw from the bag are Snickers? (Assume you are going to keep the candy bars.) Tell whether the two draws are independent or dependent



Calculate the probability.

(Round to three decimal places.)

Answer 1

1) The first thing we have to determine when calculating probability is the total number of possible outcomes and the total number of desired outcomes. In this case, our total number of possible outcomes are every combination that can be rolled using two dice. Each die has six faces numbered 1-6. If we roll one die we have 6 possible outcomes. If we roll two die we have 36 possible outcomes. But why is our total number of possible outcomes 36 and not 12? When we roll the first die we have 6 different possible outcomes. When we add the second die, we also have 6 different possible outcomes, however, we are rolling the dice together so we have to multiply the possible outcomes for each die. 6x6=36. (For more information about this you may want to explore a topic called permutations and combinations.)

 

Now that we know the total number of possible outcomes we have to calculate the total number of desired outcomes. Our first desired outcome is rolling a sum of 9 using the two dice. We can get a sum of a 9 in a number of ways as outlined in the chart below:

 

First Die : Second Die

3 : 6

4 : 5

5 : 4

6 : 3

 

As you can see in the chart above, there are only four different ways to roll a sum of 9 using two dice. So our total number of desired outcomes is 4. 

 

To calculate probability we'll divide our number of desired outcomes by the total number of possible outcomes which, in this case, would be 4 divided by 36 to 4/36. 4/36 can be simplified to 1/9 or .111 rounded to three decimal places. However, this is just the first part of the problem. Next we'll need to calculate the probability of rolling a sum of 3.

 

Do you have enough information to complete the next step and calculate the probability of rolling a 3 using two dice?