Find the Probability of Guessing Correctly at Most Three of the Seven Answers in a True Or False Objective Test. - Mathematics and Statistics

Sum

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=1/2and 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=1/2and 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

Concept: Probability Distribution of a Discrete Random Variable
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