Solving the Trinomial & Binomial Distributions: A Challenge

[engr.humayun]

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.

 

[JaredJames]

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

Jared