Question

Find the probability of guessing correctly at most three of the seven answers in a True or False objective test.

Answer 1

Let the probability of True be $p$ and he probability of False be $q$ then

$p=\frac{1}{2}$ and $q=\frac{1}{2}$

For at most three success, there might be $1$ true answer or $2$ true answers or $3$ true answers.

Therefore the required probability $\left(P\right)$ using Burnoli's probability formula as,

$={}^7{C}_0{p}^0{q}^7{+}^7{C}_{1}p{q}^6{+}^7{C}_2{p}^2{q}^5{+}^7{C}_3{p}^3{q}^4$

$=(\frac{1}{2}{)}^7+7(\frac{1}{2}{)}^7+21(\frac{1}{2}{)}^7+35(\frac{1}{2}{)}^7$

$=64(\frac{1}{2}{)}^7$

$=\frac{1}{2}.$

This is the required solution.