Use the multinomial formula and find the probabilities for each. Round your answers to at least three decimal places. n=6, X=1, X=2, X3=3, P1=0.4, P2=0.3, P3=0.3. The probability for the given multinomial is___.

Use the multinomial formula and find the probabilities for each. Round your answers to at least three decimal places. n=6, X=1, X=2, X3=3, P1=0.4, P2=0.3, P3=0.3. The probability for the given multinomial is___.

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Expert Solution

Step 1: Introduce the given information

Given information,

n = 6, X₁ = 1, X₂ = 2, X₃ = 3,

P₁ = 0.4, P₂ = 0.3, P₃ = 0.3

Using formula (Multinomial probability),

$P left parenthesis X subscript 1 equals x subscript 1 comma.. comma X subscript K equals x subscript k right parenthesis equals fraction numerator n factorial over denominator x subscript 1 factorial... x subscript k factorial end fraction. left parenthesis p subscript 1 right parenthesis to the power of x subscript 1 end exponent... left parenthesis p subscript k right parenthesis to the power of x subscript k end exponent$

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