You are taking a short 4-question pop quiz over material you forgot to study for

Question

You are taking a short 4-question pop quiz over material you forgot to study for. Each question is multiple choice with 5 possible answers. These questions are fill-n-the-blank. Be sure that you write each solution as a decimal to 4 decimal places and include a leading zero. (Example .179" should be written as "0.1790). a. The probability that you guess correctly on all 4 questions ts b. The probability that you guess incorrectly on all 4 questions c. The probability that you get at least one of the questions wrong is d. The probability that your first correct question is on the 3rd question ts

Explanation / Answer

Ans:

Probability of being a correct asnwer=1/5=0.2

n=4

Use binomial distribution with n=4,p=0.2

a)P(all correct)=P(x=4)=0.2^4=0.0016

b)P(none is correct)=P(x=0)=(1-0.2)^4=0.4096

c)P(atleast one wrong)=1-P(none is wrong)=1-P(all correct)=1-0.0016=0.9984

d)P(first correct on 3rd question)=0.8*0.8*0.2=0.1280

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