The probability of guessing correctly at least 8 out of 10 answers of a true false type examination is:
$\frac{7}{64}$
$\frac{7}{128}$
$\frac{45}{1024}$
$\frac{7}{41}$
Solution:
$\text{n}=10,\text{p = q}=\frac{1}{2}$
$\text{P(X}\geq8)=\text{P(8) + P(9) + P(10)}$
$\text{P(X}\geq8)=\text{ }^{10}\text{C}_8\big(\frac{1}{2}\big)^{10}+\text{ }^{10}\text{C}_{9}\big(\frac{1}{2}\big)^{10}+\text{ }^{10}\text{C}_{10}\big(\frac{1}{2}\big)^{10}$
$\text{P(X}\geq8)=\frac{45+10+1}{2^8}$
$\text{P(X}\geq8)=\frac{56}{256}=\frac{7}{128}$
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Then, the number of functions $g:[-1,1] \rightarrow[0,1]$ such that $(g \circ f)(x)=x$ for all $x \in[0,1]$ is
