Mark the correct alternative in the following question : The prob… - Vidyadip

MCQ

Mark the correct alternative in the following question : The probability of guessing correctly at least $8$ out of $10$ answers of a true false type examination is :

A
$\frac{7}{64}$
✓
$\frac{7}{128}$
C
$\frac{45}{1024}$
D
$\frac{7}{41}$

✓

Answer

Correct option: B.

$\frac{7}{128}$

$\text{n}=10,\text{p = q}=\frac{1}{2}$
$\text{P(X}\geq8)=\text{P(8) + P(9) + P(10)}$
$\text{P(X}\geq8)=\text{ }^{10}\text{C}_8\big(\frac{1}{2}\big)^{10}+\text{ }^{10}\text{C}_{9}\big(\frac{1}{2}\big)^{10}+\text{ }^{10}\text{C}_{10}\big(\frac{1}{2}\big)^{10}$
$\text{P(X}\geq8)=\frac{45+10+1}{2^8}$
$\text{P(X}\geq8)=\frac{56}{256}=\frac{7}{128}$

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