Question
A multiple choice examination has 5 questions. Each question has three alternative answers of which exactly one is correct. The probability that a student will get 4 or more correct answers just by guessing is:
A.
$$\frac{{17}}{{{3^5}}}$$
B.
$$\frac{{13}}{{{3^5}}}$$
C.
$$\frac{{11}}{{{3^5}}}$$
D.
$$\frac{{10}}{{{3^5}}}$$
Answer :
$$\frac{{11}}{{{3^5}}}$$
Solution :
$$p$$ = $$P$$ (correct answer), $$q$$ = $$P$$ (wrong answer)
$$ \Rightarrow \,\,p = \frac{1}{3},q = \frac{2}{3},n = 5$$
By using Binomial distribution
Required probability $$ = {\,^5}{C_4}{\left( {\frac{1}{3}} \right)^4}.\frac{2}{3} + {\,^5}{C_5}{\left( {\frac{1}{3}} \right)^5}$$
$$\eqalign{
& = 5.\frac{2}{{{3^5}}} + \frac{1}{{{3^5}}} \cr
& = \frac{{11}}{{{3^5}}} \cr} $$