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Probability (Argent) Thanks!

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Qs: A taking a multiple choice exam in which each questions four choices. A randomly drawing the four balls(marked A,B,C and D) to determine the answers. There are five multipule choice questions on the exam. What is the probability that A will get,a) five questions correct?b) at least four questions correct?c)... 顯示更多 Qs: A taking a multiple choice exam in which each questions four choices. A randomly drawing the four balls(marked A,B,C and D) to determine the answers. There are five multipule choice questions on the exam. What is the probability that A will get, a) five questions correct? b) at least four questions correct? c) no questions correct? d) no more than 2 questions correct?

最佳解答:

Let x= no. of correct answer in the exam In this question, x obeys binomial distribution P(the answer is correct on each question)=1/4 P(the answer is not correct on each question)=3/4 P(X=n)=(5Cn)*(1/4)^(n)*(3/4)^(5-n) a) P(X=5)=(5C5)*(1/4)^5*(3/4)^0 .............=(1/4)^5 .............=1/1024 b) P(X>=4)=P(X=4)+P(X=5) ...............=(5C4)*(1/4)^4*(3/4)^1 + 1/1024 ...............=5*(1/256)(3/4)+1/1024 ...............=15/1024+1/1024 ...............=1/64 c) P(X=0)=(5C0)*(1/4)^0*(3/4)^5 ..............=(3/4)^5 ..............=243/1024 d) P(X<=2)=P(X=0)+P(X=1)+P(X=2) ................=243/1024+(5C1)*(1/4)^1*(3/4)^4+(5C2)(1/4)^2(3/4)^3 ................=243/1024+5*(1/4)(81/256)+10*(1/16)(27/64) ................=243/1024+405/1024+270/1024 ................=459/512

 

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