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This is a computation of probabilities for a Bernoulli trial. Assume that n = 13, and p = 5/9. Find the probability of at least 1 success and at lea

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

This is a computation of probabilities for a Bernoulli trial. Assume that n = 13, and p = 5/9.

Find the probability of at least 1 success and at least 3 failures.

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Expert Solution

Step 1

From the given information,

n=13

p=P(success)=5/9

Let X denotes the number of successes follows Binomial with n=13 and p=5/9.

$P (X = x) = (\begin{matrix} n \\ x \end{matrix}) p^{x} {(1 - p)}^{n - x} = (\begin{matrix} 13 \\ x \end{matrix}) {\frac{5}{9}}^{x} {(1 - \frac{5}{9})}^{13 - x}$

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