Question

Probability of guessing correctly atleast $7$ out of $10$ answers in a "True" or "False" test is $=$___

• A. $\frac{11}{64}$
• B. $\frac{11}{32}$
• C. $\frac{11}{16}$
• D. $\frac{27}{32}$

Answer 1

Answer: (A)

$\frac{11}{64}$

Each question can be answered in $2$ ways (True or False)
$\therefore$ Total ways in which $10$ questions can be answered
$=2^{10}$
No. of ways of guessing at least $7$ questions out of $10$
$=7$ questions correct $+8$ questions correct $+9$ questions correct $+10$ questions correct
$={}^{10}{C}_7{\left(1\right)}^7+{}^{10}{C}_8{\left(1\right)}^8+{}^{10}{C}_9{\left(1\right)}^9+{}^{10}{C}_{10}{\left(1\right)}^{10}$
$=120+45+10+1$
$=176$
$\therefore$ Required Probability $=\frac{176}{2^{10}}$$=\frac{11\times 16}{2^{10}}$ $=\frac{11}{64}$