Answer:
Option A
Explanation:
In each true and false question , probability of guessing correctly is p= $\frac{1}{2}$ and probability of not guessing correctly , q= $\frac{1}{2}$
Here, n=0
$\therefore$ ,The probability of guessing atleast 7 correctly = P $(X\geq7)$
=P(X=7)+P(X=8)+P(X=9)+P(X=10)
= $^{10}C_{7}\left( \frac{1}{2}\right)^{7}\left(\frac{1}{2}\right)^{3}+^{10}C_{8}\left( \frac{1}{2}\right)^{8}\left(\frac{1}{2}\right)^{2}+^{10}C_{9}\left( \frac{1}{2}\right)^{9}\left(\frac{1}{2}\right)^{1}+^{10}C_{10}\left( \frac{1}{2}\right)^{10}$
$[\because P(x=r)=^{n}C_{r}p^{r}q^{n-r}]$
= $120\times(\frac{1}{2})^{10}+45\left(\frac{1}{2}\right)^{10}+10\left( \frac{1}{2}\right)^{10}+1\left( \frac{1}{2}\right)^{10}$
=$\frac{120+45+10+1}{2^{10}}=\frac{176}{1024}=\frac{11}{64}$
