Extension on a simple probability question

In summary, the conversation discusses techniques for finding the number of sample points in a probability problem involving tossing dice. The first technique mentioned is to define a discrete random variable and compute the probability mass function. The other technique mentioned is to use counting methods such as combinations and permutations.
  • #1
trap101
342
0
An experiment consists of tossing a pair of dice:

1) Determine the number of sample points in the sample space

2) Find the probability that the sum of the numbers appearing on the dice is equal to 7


Issue: Ok so I know how to do this problem, but my question comes with respect to the second portion. In this specific problem I am able to count the different sample points that make the dice add up to 7 i.e: 6/36 is the answer, but what if this was a larger problem? e.g: Say that instead of 2 dice I had 7 dice and I needed to find the probability of the seven dice adding up to 15...What technique would I have to use to find/count all those sample points? It surely can't be by counting each one individually?
 
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  • #2
There are always many different techniques to solve probability problems. For example, I could define a discrete random variable S as the sum of 7 i.i.d. uniform random variables X~U[1,6]. Then, I could compute the probability mass function of S with 7 discrete convolutions, with the answer being F_S(15) where F_S is the pmf of S.

You can also use counting methods (combinations, permutations, etc.).
 
  • #3
RoshanBBQ said:
There are always many different techniques to solve probability problems. For example, I could define a discrete random variable S as the sum of 7 i.i.d. uniform random variables X~U[1,6]. Then, I could compute the probability mass function of S with 7 discrete convolutions, with the answer being F_S(15) where F_S is the pmf of S.

You can also use counting methods (combinations, permutations, etc.).





Ahhh. You see I haven't reached that part of my text yet. I looked through it but haven't done any of the work involving those concepts, but now I see what your getting at. Thanks
 

FAQ: Extension on a simple probability question

1. What is the definition of probability?

Probability is a measure of the likelihood of an event occurring. It is represented as a number between 0 and 1, where 0 indicates impossibility and 1 indicates certainty.

2. What is the difference between simple probability and compound probability?

Simple probability involves the likelihood of a single event occurring, whereas compound probability involves the likelihood of multiple events occurring together.

3. How is probability calculated?

Probability is calculated by dividing the number of favorable outcomes by the total number of possible outcomes. This can be represented as a fraction, decimal, or percentage.

4. What is the role of sample size in probability?

Sample size refers to the number of observations or data points in a given sample. In probability, a larger sample size generally leads to more accurate and reliable results.

5. Can probability be greater than 1?

No, probability cannot be greater than 1. A probability of 1 represents certainty, and anything greater than 1 would indicate a greater than 100% chance of an event occurring, which is not possible.

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