A multiple choice examination has 5 questions. Each question has three alternative answers of which exactly…
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 at least one correct answer is
$\frac{80}{243}$
$\frac{32}{243}$
$\frac{163}{243}$
$\frac{211}{243}$
Solution
There are 5 questions and each question has 3 options of which one is correct. $\therefore$ Probability of getting correct answer $=\frac{1}{3}$
Thus $\mathrm{n}=5, \mathrm{p}=\frac{1}{3}, \mathrm{q}=\frac{2}{3}$
$P$ (at least one correct answer)
$=1-P($ None is correct $)$
$=1-{ }^{5} C_{0}\left(\frac{1}{3}\right)^{0}\left(\frac{2}{3}\right)^{5}=1-1 \times 1 \times \frac{32}{243}$ $=\frac{243-32}{243}=\frac{211}{243}$