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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`
=`(1/2)^7+7(1/2)^7+21(1/2)^7+35(1/2)^7`
=`64xx(1/2)^7`
= `64/128`
=`1/2`
= 0.5
∴ 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+"^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`
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