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Solution for Find the Probability of Guessing Correctly at Most Three of the Seven Answers in a True Or False Objective Test. - HSC Commerce 12th Board Exam - Mathematics and Statistics

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Question

Find the probability of guessing correctly at most three of the seven answers in a True or False objective test. 

Solution 1

For true, false question
Let the prob. of true p=`1/2`and q=`1-p=1-1/2=1/2` 

Now we have to find 

`p(x<=)=p(0)+p(1)+p(2)+p(3)`

=`""^7C_0(1/2)^0(1/2)^7+""^7C_1(1/2)(1/2)^6+"^7C_2(1/2)^2(1/2)^5+^7C_3(1/2)^3(1/2)^4` 

=`(1/2)^7+7(1/2)^7+21(1/2)^7+35(1/2)^7` 

=`64xx(1/2)^7` 

=`1/2` 

∴ Prob. of guessing at most three question 

correctly = `1/2` 

 

Solution 2

For true, false question
Let the prob. of true p=`1/2`and q=`1-p=1-1/2=1/2` 

Now we have to find 

`p(x<=)=p(0)+p(1)+p(2)+p(3)`

=`""^7C_0(1/2)^0(1/2)^7+""^7C_1(1/2)(1/2)^6` 

=`(1/2)^7+7(1/2)^7+21(1/2)^7+35(1/2)^7` 

=`64xx(1/2)^7` 

=`1/2` 

∴ Prob. of guessing at most three question 

correctly = `1/2` 

 

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APPEARS IN

 2017-2018 (March) (with solutions)
Question 6.2.1 | 4.00 marks

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Solution Find the Probability of Guessing Correctly at Most Three of the Seven Answers in a True Or False Objective Test. Concept: Probability Distribution of a Discrete Random Variable.
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