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1. In a large population, 10% of individuals have certain disease. If 20 individuals are selected randomly,

1. In a large population, 10% of individuals have certain disease. If 20 individuals are selected randomly,

A First Course in Probability (10th Edition)
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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1. In a large population, 10% of individuals have certain disease. If 20 individuals are selected randomly, (a) what is the probability that exactly 5 individuals have the disease? (b) what is the probability that not more than 5 have the disease? The probability that at least 2 do? (c) Find the expected number of people that have the disease.
Transcribed Image Text:1. In a large population, 10% of individuals have certain disease. If 20 individuals are selected randomly, (a) what is the probability that exactly 5 individuals have the disease? (b) what is the probability that not more than 5 have the disease? The probability that at least 2 do? (c) Find the expected number of people that have the disease.
Expert Solution
Step 1: Writing given data

Given that 

in a large population, 10% of individuals have certain disease.

20 individuals are selected randomly.

Here,

sample size (n) = 20

Probability of having a disease (P) = 0.10

Here, only two options are there for people having that disease or not having Thus, Binomial probability distribution is best suited for this.

We know that

Binomial probability distribution P(X=x) = nCx x Px x (1-P)(n-x)

Expected value E(x)  = n x P


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