#### 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

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.