Solving the Trinomial & Binomial Distributions: A Challenge

In summary: Hi, can anyone help me solve this problem regarding the Binomial and Trinomial distributions?In summary, the conversation is about a problem involving the calculation of probabilities using the Binomial and Trinomial distributions. The first part involves finding the probability of k successes, j fails, and (n-(k+j)) unknown outcomes in an experiment with 3 possible outcomes. The second part involves calculating the probabilities of different combinations of states for 5 indicator lights with different probabilities.
  • #1
engr.humayun
1
0
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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  • #2


Can you please show your attempt at a solution as per the PF guidelines.

Jared
 

Related to Solving the Trinomial & Binomial Distributions: A Challenge

1. What is the difference between trinomial and binomial distributions?

Trinomial and binomial distributions are both types of probability distributions. The main difference between them is the number of possible outcomes. A binomial distribution has two possible outcomes, while a trinomial distribution has three possible outcomes.

2. How do you solve a trinomial distribution?

To solve a trinomial distribution, you need to first determine the probability of each outcome. Then, you can use the formula P(x) = nCx * p^x * q^(n-x) to calculate the probability of getting exactly x successes in n trials. Finally, you can add up the probabilities for all possible values of x to get the overall probability distribution.

3. Can trinomial and binomial distributions be used in real-life scenarios?

Yes, trinomial and binomial distributions can be used to model real-life situations. For example, a binomial distribution can be used to model the probability of success in a series of independent trials, such as flipping a coin or rolling a die. A trinomial distribution can be used to model situations with three possible outcomes, such as predicting the outcome of a sports game with three possible outcomes (win, lose, or tie).

4. What are some common applications of trinomial and binomial distributions?

Trinomial and binomial distributions have many practical applications in various fields such as statistics, economics, and biology. Some common applications include quality control in manufacturing, market research, and risk assessment in finance.

5. Is there a specific formula for solving binomial distributions?

Yes, there is a specific formula for solving binomial distributions. It is P(x) = nCx * p^x * q^(n-x), where n is the number of trials, x is the number of successes, p is the probability of success, and q is the probability of failure (1-p). This formula can be used to calculate the probability of getting exactly x successes in n trials of a binomial experiment.

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