High School Probability IB Math HL: Is it a difficult question to solve?

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SUMMARY

The discussion centers on calculating the probability of drawing 8 cards from a set of 117 cards numbered 1 to 6, with the goal of achieving a sum of 28. The probabilities for each card number are provided: P(1)=8/117, P(2)=14/117, P(3)=34/117, P(4)=39/117, P(5)=14/117, and P(6)=8/117. Participants suggest that solving this problem requires extensive casework due to the complexity of combinations without replacement. A recommended approach is to utilize a computer program to enumerate all combinations that yield the desired sum.

PREREQUISITES
  • Understanding of combinatorial probability
  • Familiarity with the concept of drawing without replacement
  • Basic programming skills for algorithm implementation
  • Knowledge of probability distributions for discrete variables
NEXT STEPS
  • Implement a program to generate combinations of 8 cards that sum to 28
  • Study combinatorial probability techniques for problems involving sums
  • Explore the use of recursive algorithms for generating combinations
  • Learn about probability mass functions in discrete distributions
USEFUL FOR

Students studying IB Math HL, educators teaching probability concepts, and anyone interested in advanced combinatorial problems.

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I have not been able to figure out the solution. Can anyone help me with this?

A person picks 8 cards without replacement from a bag containing cards numbered from 1 to 6 (117 in total). What is the probability that the sum of those 8 cards is 28? Given that P(1)=8/117, P(2)=14/117, P(3)=34/117, P(4)=39/117. P(5)=14/117 and P(6)=8/117.
A person picks 8 cards without replacement from a bag containing cards numbered from 1 to 6 (117 in total). What is the probability that the sum of those 8 cards is 28? Given that P(1)=8/117, P(2)=14/117, P(3)=34/117, P(4)=39/117. P(5)=14/117 and P(6)=8/117.
 
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Where does this problem come from?
What did you try so far?
This will probably need ugly casework. With replacement it would be much easier.
 
coolfish21 said:
Summary:: I have not been able to figure out the solution. Can anyone help me with this?

A person picks 8 cards without replacement from a bag containing cards numbered from 1 to 6 (117 in total). What is the probability that the sum of those 8 cards is 28? Given that P(1)=8/117, P(2)=14/117, P(3)=34/117, P(4)=39/117. P(5)=14/117 and P(6)=8/117.

A person picks 8 cards without replacement from a bag containing cards numbered from 1 to 6 (117 in total). What is the probability that the sum of those 8 cards is 28? Given that P(1)=8/117, P(2)=14/117, P(3)=34/117, P(4)=39/117. P(5)=14/117 and P(6)=8/117.
I suggest you write a computer program to do it.
 
First step: list all combination which add to 28. The probability in each case is straightforward. Then add.
 

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