Question

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

Answer 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` 

Answer 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`