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Taking an Exam

Given

Number of questions (n 10

Probability of getting correct answer on guess (p 1 /5 (each question has 5 answers

Probability of getting wrong answer on guess (1 -

1 - 1 /5 4 /5

The Binomial Distribution : the probability of a success for a single trial of a probability experiment Where , x is the number of successes (1 , 2 , 3 .n

Pascal Gonoyo gets exactly 2 questions correct

x 2 , therefore ( 0 .30199

Pascal Gonoyo gets no questions correct

x 0 , therefore (0 .10737

p Since , the probability of not getting any correct answer is 0 , therefore probability of getting at least one correct answer will be 1 - 0 .10737 0 .89263

Pascal Gonoyo gets at least 9 questions correct

For getting , at least nine question correct he has to get exactly 9 or 10 questions correct

Therefore ( 0 .6 0 (0

Pascal Gonoyo gets exactly 2 questions correct (without using The Binomial Distribution

2 right answers (or 8 wrong answers ) can be found from 10 questions by selecting 2 questions from 10 questions with correct answers

ways

Now , for getting right answers these 2 questions should be right and at the same time all other questions should be wrong so that exactly 2 correct answers comes

Since , outcomes of each questions are independent to each other therefore the probability for getting correct answers will be (number of ways of selection of 2 questions (probabili ? 0 .30199

Comparison of answers to part (a ) and part (e

Both answers are same as 0 .30199

The reason for this is that this experiment satisfies the Binomial Distribution (binomial experiment , which is given below (R -

A

M

N

O

Y

E

YU

N

Y

E

YU

b

w

sch

y

stion , correct and wrong . Depending on the situation , either correct or wrong can be defined as a success and the other as a failure

There is a fixed number of trials (10 questions

The outcomes of each trial are independent of each other

The probability of a success (getting correct answer ) is 0 .2 and it does not change and remains same for each question...