Solving the Trinomial & Binomial Distributions: A Challenge

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SUMMARY

The discussion focuses on deriving the Trinomial distribution formula and solving specific probability problems related to indicator lights. The Binomial distribution is initially described, emphasizing its application in calculating probabilities of success and failure in experiments with two outcomes. The challenge extends to a scenario with three outcomes, requiring the formulation of the Trinomial distribution. Additionally, participants are tasked with calculating probabilities for a set of independent indicator lights with defined states and probabilities.

PREREQUISITES
  • Understanding of Binomial distribution and its formula
  • Knowledge of Trinomial distribution concepts
  • Familiarity with probability theory and independent events
  • Ability to manipulate factorial expressions in probability calculations
NEXT STEPS
  • Study the derivation of the Trinomial distribution formula
  • Learn how to calculate probabilities for independent events
  • Explore advanced probability concepts such as conditional probability
  • Practice solving problems involving multiple outcomes in probability distributions
USEFUL FOR

Students and professionals in statistics, data science, and mathematics who are looking to deepen their understanding of probability distributions, particularly those dealing with multiple outcomes and independent events.

engr.humayun
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can anyone help me please

can anyone solve this problem for me please

Q) The Binomial distribution allows the calculation of the probability of k successes in n trails where there are only two outcomes: success or fail with probabilities p and q respectively. The Binomial probability is given by

n! / (n-k)! * p k q n-k ( / is division sign)

a) Consider a case where an experiment has 3 possible outcomes (success, fail, unknown) with probabilities p , q and r respectively. Derive a formula for the Trinomial distribution i.e. the probability of getting k success, j fail and (n-(k+j)) unknown outcomes from a sequence of n trails.

b) An indicator light can be in one of three states: OFF, FLASHING and ON, with probabilities 1/ 2 , 2 /5 and 1 /10 respectively. A test panel has 5 such lights whose states are mutually independent.

i. What is the probability that all five lights are OFF?
ii. What is the probability that three lights are OFF, one light is FLASHING and one light
is ON?
iii. What is the probability that three or more lights are OFF and at most one is ON?

Express all results as fractions.
 
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Can you please show your attempt at a solution as per the PF guidelines.

Jared
 

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