Combanatorics Problem (Probability Application)

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SUMMARY

The forum discussion centers on a combinatorics problem involving the probability of shipping Panasonic tape recorders. The calculations provided by the user indicate that the probability of both tape recorders being sent to L.A. is 0.4857, derived from the formula (35 choose 2)/(50 choose 2). Additionally, the probability of one tape recorder going to L.A. and the other to Miami is calculated as 0.4286, using the formula [(35 choose 1)(15 choose 1)]/(50 choose 2). These results demonstrate a solid understanding of combinatorial probability.

PREREQUISITES
  • Understanding of combinatorial mathematics, specifically combinations
  • Familiarity with probability theory and its applications
  • Basic knowledge of Panasonic tape recorders and their distribution logistics
  • Ability to perform calculations involving factorials and binomial coefficients
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  • Study advanced combinatorial techniques, such as permutations and their applications
  • Explore probability distributions and their significance in real-world scenarios
  • Learn about the binomial theorem and its relationship to combinatorial problems
  • Investigate practical applications of probability in logistics and supply chain management
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This discussion is beneficial for students studying combinatorics, educators teaching probability concepts, and professionals in logistics and supply chain management who require a solid understanding of probability calculations.

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Homework Statement

From a load of 50 Panasonic tape recorders 35 are destined for L.A. and 15 are destined fro Miami. If two are shipped to Trenton by mistake and the "selection" is made at random, determine the probabilities that:

a) both should have gone to L.A.

b) one should have gone to L.A. and the other to Miami



Homework Equations





The Attempt at a Solution

Alright, I think I'm starting to get the hang of these. But I want to bounce this one off of somebody to get a second set of eyes on it.

For P(both to L.A.) I am getting (35 choose 2)/(50 choose 2) = 0.4857

For P(one to each city) I am getting [(35 choose 1)(15 choose 1)]/(50 choose 2) = 0.4286
 
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