Question

Assignment Details

Think about situations or types of problems where probabilities are useful.

1. Describe a specific situation/problem involving probabilities.
2. Explain how and why probabilities might be useful in this situation.  
3. Give a specific example of how probabilities are used in this situation.  
4. How are probabilities important to decision making in this situation? If they are not, then discuss why not.

Answer 1

Suppose you are playing Lucky 7 game where the 2 dices are to be rolled together and the sum of both the dices will be the number for which you can bet.

There are 3 parts where you can bet on the table

1)If you bet for the sum of dice < 7 you will get twice the money

2)If you bet for the sum of dice > 7 you will get twice the money

3)If you bet for the sum of dice = 7 you will get thrice the money

Now if we need to view the same on the probability table

first check for instances of possible outcome

Now the sum of each cells will give us some of dice

So the total count of 2 = 1

the total count of 3 = 2

the total count of 4 = 3

the total count of 5 = 4

the total count of 6 = 5

the total count of 7 = 6

the total count of 8 = 5

the total count of 9 = 4

the total count of 10 = 3

the total count of 11 = 2

the total count of 12 = 1

Hence the associated probabilities are

for sum=2 it is 1/36

for sum=3 it is 2/36

for sum=4 it is 3/36

for sum=5 it is 4/36

for sum=6 it is 5/36

for sum=7 it is 6/36

for sum=8 it is 5/36

for sum=9 it is 4/36

for sum=10 it is 3/36

for sum=11 it is 2/36

for sum=12 it is 1/36

And now we can say that Prob(sum<7) =(1+2+3+4+5)/36=15/36=5/12

Prob(sum=7) =6/36=1/6

Prob(sum>7) =(1+2+3+4+5)/36=15/36=5/12

Hence the probabilities can help us take informed decision and in this case we can say that the game is not even as by betting anywhere you are not having probability of win =0.5

So the probabilities are important here to take a call whether it's an even game or you are bound to loose in the long run.

Hope the above answer has helped you in understanding the problem. Please upvote the ans if it has really helped you. Good Luck!!