A white goose hunter kills 60% of the geese he kills he shoots. Calculate the probability that with his next 10 shots he kills at least 7 geese. Find the expectation and variance of number of geese shot in these 10 shots

A white goose hunter kills 60% of the geese he kills he shoots. Calculate the probability that with his next 10 shots he kills at least 7 geese. Find the expectation and variance of number of geese shot in these 10 shots

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

A white goose hunter kills 60% of the geese he kills
he shoots. Calculate the probability that with his next 10 shots he
kills at least 7 geese. Find the expectation and variance of
number of geese shot in these 10 shots

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Expert Solution

Step 1: Information given is

Probability that a white goose hunter kills the geese(p)=0.60

sample size(n)=10

Let "x" be that the no. of geese that the goose hunter kills

x~Binomial(n=10,p=0.60)

P(X=x)= $open parentheses table row straight n row straight x end table close parentheses cross times straight p to the power of straight x cross times left parenthesis 1 minus straight p right parenthesis to the power of straight n minus straight x end exponent space space space semicolon space straight x equals 0 comma 1 comma.. comma straight n$

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