Question

A multiples choice test contain 10 questions. Each question have five choice for the correct answer only one choice is correct what is the probability of making exactly 80% with random guessing
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Answer 1

Answer:-

$\sf{The \ probability \ of \ making \ exactly \ 80\%}$

$\sf{with \ random \ guessing \ is \ 0.08}$

Given:

• A multiples choice test contain 10 questions.

• Each question have five choice for the correct answer only one choice is correct.

To find:

• Probability of making 80%

Solution:

$\sf{Let \ 10 \ questions \ be \ A, \ B, \ C, \ D \ E,...,J}$

$\sf{In, \ question \ A \ there \ are \ 5 \ sub \ questions}$

$\sf{also, \ any \ one \ option \ can \ be \ right. }$

$\sf{Let \ right \ answer \ start \ with \ R \ and \ wrong}$

$\sf{answer \ start \ with \ W}$

$\sf{Let \ A \ be \ the \ set \ of \ outcomes \ of \ question \ A}$

$\sf{\therefore{A=\{RA_{1}, \ RA_{2}, \ RA_{3}, \ RA_{4}, \ RA_{5},}}$

$\sf{WA_{1}, \ WA_{2}, \ WA_{3}, \ WA_{4}, \ WA_{5}\}}$

$\sf{\therefore{n(A)=10}}$

$\sf{In \ the \ same \ way,}$

$\sf{All \ 10 \ questions \ will \ have \ 10 \ outcomes \ each.}$

$\sf{Let \ S \ be \ the \ set \ of \ outcomes \ for \ all \ questions. }$

$\sf{\therefore{n(S)=100}}$

_______________________________________

$\sf{80\% \ of \ 10 \ is \ 8}$

$\sf{It \ means \ 8 \ chosen \ option \ must \ be \ correct.}$

$\sf{Let \ R \ be \ set \ of \ 8 \ correct \ chosen \ options. }$

$\sf{\therefore{n(R)=8}}$

$\sf{Probability \ of \ happening \ event \ R \ is}$

$\sf{P(R)=\frac{n(R)}{n(S)}}$

$\sf{\therefore{P(R)=\frac{8}{100}}}$

$\sf{\therefore{P(R)=0.08}}$

$\sf\purple{\tt{\therefore{The \ probability \ of \ making \ exactly \ 80\%}}}$

$\sf\purple{\tt{with \ random \ guessing \ is \ 0.08}}$