5. The Binomial random variable's probability mass(density) function is:n!p(i)=(n-ili!• Suppose that four fair coins are flipped. If the outcomes are assumed independent, what is theprobability that two heads and two tails are obtained?• Itis known that any item produced by a certain machine will be defective with probability 0.1,independently of any other item. What is the probability that in a sample of three items, at mostone will be defective?

5. The Binomial random variable's probability mass(density) function is: n! p(i)=|" |p'(1– p)', i = 01... where (n- i}!i! Suppose that four fair coins are flipped. If the outcomes are assumed independent, what is the probability that two heads and two tails are obtained?

5. The Binomial random variable's probability mass(density) function is: n! p(i)=|" |p'(1– p)', i = 01... where (n- i}!i! Suppose that four fair coins are flipped. If the outcomes are assumed independent, what is the probability that two heads and two tails are obtained?

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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Question

5. The Binomial random variable's probability mass(density) function is:
n!
p(i)=
(n-ili!
• Suppose that four fair coins are flipped. If the outcomes are assumed independent, what is the
probability that two heads and two tails are obtained?
• Itis known that any item produced by a certain machine will be defective with probability 0.1,
independently of any other item. What is the probability that in a sample of three items, at most
one will be defective?

Expert Solution

Step 1

The binomial random variables probability mass function is,

$p (i) = (\begin{matrix} n \\ i \end{matrix}) p^{i} {(\begin{matrix} 1 - & p \end{matrix})}^{n - 1} i = o, 1, 2 . . . . n$

where, $(\begin{matrix} n \\ i \end{matrix}) = \frac{n!}{(n - 1)! i!}$

(1) solution : given,

n = 4

p = 0.5

r = 2

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