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

The correct option is A $\frac{11}{64}$

It is a binomial distribution where success is guessing the right answer, and probability of guessing the right answer is $0.5$.

So here $p=0.5$ , $q=0.5$ and $n=10$

we have to find $P(X\ge 7)$

$={}^{10}{C}_7(0.5{)}^{10}+{}^{10}{C}_8(0.5{)}^{10}+{}^{10}{C}_9(0.5{)}^{10}+{}^{10}{C}_{10}(0.5{)}^{10}$

$=(0.5{)}^{10}\times (176)$

$=\frac{11}{64}$

answer (a).