Chapter oS, Section 5.5, Problem 045 A realy bad carton of 18 eggs contains 6 sp

Question

Chapter oS, Section 5.5, Problem 045 A realy bad carton of 18 eggs contains 6 spoiled eggs. An unsuspecting chef picks 3 eggs at random for his "Hegs-Omalet Surprise. Find the probubility thuat the number of unspoiled eggs among the 3 solected is a. exactly 3 Round your answer to four decimal places Piexactly 3)-? b, 2 or fewer Round your answer to four decimal places. Pr2or fewer) c. more than Round your answer to four decimal places. P( more than 1)- Click if you would like to Show Work for this question: 0pn 5ho Work

Explanation / Answer

Ans:

Probability of being a spoiled egg,p=6/18=1/3

Use binomial distribution with n=3,p=1/3

a)

P(exactly 3)=P(x=3)=(1/3)^3=1/27=0.0370

b)

P(2 or fewer)=P(x<=2)=1-P(x=3)=1-0.0370=0.9630

c)

P(more than 1)=P(x>1)=P(x=2)+P(x=3)

=3C2*(1/3)^2*(2/3)+0.0370

=0.2222+0.0370

=0.2593

x p(x) 0 0.2963 1 0.4444 2 0.2222 3 0.0370

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